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In this paper, we investigate the non-confluence property of a class of stochastic differential equations with Markovian switching driven by fractional Brownian motion with Hurst parameter H ∈ (1 / 2 , 1) . By using the generalized Itô formula and stopping time techniques, we obtain some sufficient conditions ensuring the non-confluence property for the considered equations. Additionally, we present two important corollaries on the non-confluence property by the Poisson equation and M-matrix, respectively, which can verify the non-confluence property more effectively than the general condition. Finally, we provide an example to illustrate the practical usefulness of our theoretical results. [ABSTRACT FROM AUTHOR]

While the original Ait-Sahalia interest rate model has been found to be of considerable use for describing the time-series evolution of interest rates, it may not possess adequate specifications to explain the responses of interest rates to empirical phenomena such as volatility skew-smile effect, jumps, market regulatory lapses, economic crises, financial clashes, and political instability, among others collectively. In this article, we propose a modified version of this model by incorporating additional features to help collectively describe these empirical phenomena adequately. Since the proposed model does not have a closed-form formula, we construct new techniques of the truncated EM method to study it and justify the method within a Monte Carlo framework to compute some financial quantities. [ABSTRACT FROM AUTHOR]

This study presents a consensus control method for generic linear multi-agent systems (MASs) subject to stochastic deception attacks on actuators and random denial of service (DoS) attacks over communication channels. In this case, the MASs are communicating over a compromised network where the attackers are performing random DoS attacks and injecting data into the control inputs. A fully-distributed robust-adaptive consensus protocol is designed for both types of stochastic cyber-attacks by taking into account the immediate partial information per node rather than global information and by accounting for the signals added by adversaries. To the best of the authors' knowledge, a fully-distributed consensus control approach with adaptive gains (without requiring any global knowledge for the design) under hybrid cyber-attacks of stochastic nature over a directed graph has been addressed for the first time. Finally, simulation results are presented to further illustrate the theoretical results' effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, the μ-state estimation issue for Markovian switching complex-valued neural networks with mixed delays has been addressed. To conserve communication resources, an effective event-triggered mechanism is proposed, which relays on a Markovian switching positive threshold. By resorting to Lyapunov stability theory, stochastic analysis method and matrix inequalities technique, some sufficient criteria are established to guarantee the estimation error system is stochastic μ-stable in the mean sense. Moreover, the expected estimator gain matrices can be accurately achieved by solving some obtained matrix inequalities. Besides, it is should be pointed that the μ-stability involves exponential, power, and logarithmic stability, which expands a mass of existed relevant results. In the end, for power stability, one numerical example is provided to substantiate the effectiveness and credibility of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

Hybrid stochastic differential equations (HSDEs) have wide range of real-world applications. In this paper, we study a new kind of nonlinear delayed neutral stochastic differential equations with Markovian switched noises (NHSDE-MSN). Under the assumption that this type of equations satisfies the locally Lipschitz condition and general condition of monotonicity, the existence and uniqueness of global solutions are established. Then, based on the Lyapunov function, M-matrix theory, stochastic analysis techniques, and Barbalat lemma, taking into account the delay as a bounded function, different decay stabilities of solutions are investigated. Finally, a numerical example is given to illustrate the utility of the main results. [ABSTRACT FROM AUTHOR]

This work addresses the global exponential stability of nonlinear delayed discrete-time systems with Markovian switching. By a novel approach, some explicit criteria for the exponential stability in mean square of such systems are derived. An application to discrete-time neural networks is presented. [ABSTRACT FROM AUTHOR]

New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments are provided to show the efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we concern the strong convergence and stability of the balanced Euler method for stochastic pantograph differential equations with Markovian switching (SPDEs-MS). We present the balanced Euler method of SPDEs-MS and consider its moment boundedness under polynomial growth condition plus Khasminskii-type condition. We also study its strong convergence order and its mean-square stability. Two numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the mean exit time and the scale function for the geometric Brownian motion with Markovian switching, in which the drift coefficients and the diffusion coefficients are associated with regime changes. The explicit expressions of mean exit time and scale function are obtained by solving the corresponding Poisson problem. Furthermore, we estimate parameters for the geometric Brownian motion with Markovian switching by composite likelihood and explore some properties of the estimates. Computer simulations are performed to illustrate our proposed algorithm, showing high accuracy of the estimators. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis and verification of uniform moment exponential stability for a class of nonautonomous stochastic hybrid systems (SHSs), which contain not only continuous flows described by stochastic differential equations, but also Markovian switching and Poisson jump together. To start with, taking advantage of multiple Lyapunov functions (MLFs), we propose a necessary and sufficient condition for uniform $ p $th moment exponential stability of nonlinear nonautonomous SHSs, in which indefinite scalar function is utilized to relax the conservativeness of the classical MLFs. Then, for linear nonautonomous SHSs, we further present a necessary and sufficient condition, described by verifiable time-varying linear matrix inequalities, for uniform mean square exponential stability by our less conservative MLFs and indefinite scalar function based method. Finally, we investigate the mechanical verification of the above two conditions for rational SHSs by proposing a semi-definite programming based computable approach. The applicabilities of both our theoretical results and mechanical approach are demonstrated by academic examples. [ABSTRACT FROM AUTHOR]

Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markovian switching for additive noises is studied for an incompressible fluid flow in a bounded domain. The objective of this article is to prove the existence and identification of a stationary measure for such stochastic systems. To achieve this goal, a family of regularized equations is introduced in order to investigate the asymptotic behavior of their solutions. The existence of an ergodic measure for the regularized system is established by the Krylov-Bogolyubov method. The existence and identification of a stationary measure corresponding to the original system are obtained as a sequential limit point of the family of the ergodic measures that correspond to the regularized systems. The main result of this work is that under mild integrability conditions on the initial data and external force, there exists a stationary measure for the solution of the three-dimensional stochastic Navier-Stokes equations with Markovian switching. [ABSTRACT FROM AUTHOR]

In this paper, the low energy cost synchronization control strategy of Markovian switching complex systems/networks is mainly studied and analyzed through multiple perspectives. Firstly, in order to achieve synchronization of Markovian switching complex networks with low energy cost, a control scheme based on the optimal node selection strategy that does not depend on the network coupling strength is improved, and a finite-time controller with a simpler structure is constructed. Secondly, based on the event-triggered control strategy an effective trigger event is designed to achieve the low energy cost synchronization of Markovian switching complex networks on the basis of reducing the information transmission and interaction between networks. Finally, the two control strategies mentioned in this paper are compared and analyzed from multiple perspectives through numerical simulations to better guide practical engineering. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite‐time stabilization of a class of nonlocal Lipschitzian stochastic nonlinear systems with Markovian switching and stochastic inverse dynamics. We first present the finite‐time stability theory for stochastic nonlinear systems with Markovian switching under the framework of weak solutions. Then, a finite‐time controller with state feedback is constructed for a class of stochastic high‐order nonlinear systems with Markovian switching and stochastic inverse dynamics. The trivial weak solution of the closed‐loop system is proved to be globally finite‐time stable in probability. Finally, the effectiveness of the proposed design method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dynamics of stochastic lattice systems with Markovian switching. Based on the well-posedness of solutions, we first prove the ergodicity of invariant measures and show that the Markov chain facilitates the existence of invariant measures. In order to investigate numerical invariant measures, the convergence of invariant measures is considered between the original systems and their finite-dimensional truncated systems. Due to this, we can use the backward Euler-Maruyama method to approximate invariant measures for such infinite-dimensional systems. This work provides a feasible path for the convergence of the finite-dimensional numerical invariant measures to the analytical invariant measure. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronisation and topology identification of stochastic delayed multi-group models with multi-dispersal and Markovian switching (SDMM). Our model is characterised by a combination of the stochastic perturbation, multi-dispersal and Markovian switching, which can reasonably model the actual system. By utilising the graph theory, Lyapunov method and stochastically finite-time attractiveness, two sufficient criteria are obtained to ensure the topology identification of SDMM and finite-time topology identification of SDMM based on adaptive synchronisation and finite-time synchronisation, respectively. These criteria are closely related to the topology property of the network and can be easily verified in practice. Finally, two numerical examples are given to show the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction–diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction–diffusion neural networks with stochastic noise and Markovian switching are given. [ABSTRACT FROM AUTHOR]

For a kind of regime-switching jump diffusion process (X t , Z t) t ≥ 0 , under some conditions, it is exponentially ergodic under the weighted total variation distance with ergodic measure μ . We use the Euler–Maruyama scheme of the process (X t , Z t) t ≥ 0 which has an ergodic measure μ η (η is the step size of the Euler–Maruyama scheme) to approximate the ergodic measure μ . Furthermore, we use Stein's method to prove that the convergence rate of μ η to μ is η 1 2 in terms of some function-class distance d G (μ , μ η) . [ABSTRACT FROM AUTHOR]

In this paper, we study the averaging principle for a class of slow-fast stochastic differential equations with Markovian switching, where the slow component is the solution of a stochastic differential equation and the fast component is a Markov chain. Using the technique of Poisson equation and mollifying approximation, the optimal strong convergence order $ 1/2 $ is obtained under the Lipschitz continuous condition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching. Under the influence of impulsive disturbance, the solution for the system is discontinuous. By using the Razumikhin technique and stochastic analysis approaches, as well as combining the idea of mathematical induction and classification discussion, some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained. The stability conclusion is full time-delay. The results show that impulse, the point distance of impulse and Markovain switching affect the stability for the system. Finally, two examples are provided to illustrate the effectiveness of the results proposed. [ABSTRACT FROM AUTHOR]

New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments are provided to show the efficiency and accuracy.

This work focuses on the parameter estimation for a class of switching diffusion processes which contains a continuous component and a discrete component. Under suitable conditions, we adopt the least square method to deal with the parameter estimation of stochastic differential equations with Markovian switching. More precisely, we first prove the consistency and the asymptotic distributions of the parameter estimator of least squares when $ \varepsilon\rightarrow0 $ and $ \Delta\rightarrow0 $. Then, we present an example of numerical simulation to illustrate the correctness of the results. [ABSTRACT FROM AUTHOR]

This study is devoted to investigate the almost sure stability of a class of nonlinear delay hybrid stochastic system driven by Lévy noise. We derive that the system has a unique global solution. Then, we discuss the almost sure stability of the stochastic system. A numerical example is provided to verify the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the dynamical behavior of non-autonomous stochastic lattice systems with Markovian switching. We first show existence of an evolution system of measures of the stochastic system. We then study the pullback (or forward) asymptotic stability in distribution of the evolution system of measures. We finally prove that any limit point of a tight sequence of an evolution system of measures of the stochastic lattice systems must be an evolution system of measures of the corresponding limiting system as the intensity of noise converges zero. In particular, when the coefficients are periodic with respect to time, we show every limit point of a sequence of periodic measures of the stochastic system must be a periodic measure of the limiting system as the noise intensity goes to zero. [ABSTRACT FROM AUTHOR]

This paper concerns the dynamics of two stochastic hybrid delay Lotka-Volterra systems with harvesting and Lévy noise in a polluted environment (i.e., predator-prey system and competitive system). For every system, sufficient and necessary conditions for persistence in mean and extinction of each species are established. Then, sufficient conditions for global attractivity of the systems are obtained. Finally, sufficient and necessary conditions for the existence of optimal harvesting strategy are provided. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the dynamic behaviors and optimal harvesting strategy are closely correlated with both time delays and three types of environmental noises (namely white Gaussian noises, telephone noises and Lévy noises).

Little work seems to be known about stabilization results of highly nonlinear stochastic time-varying delay systems (STVDSs) with Markovian switching and Poisson jump. This paper is concerned with the stabilization problem for a class of STVDSs with Markovian switching and Poisson jump. The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. The aim of this paper is to design a delay feedback controller to make an unstable highly nonlinear STVDSs with Markovian switching and Poisson jump $H_\infty$-stable and asymptotically stable. Besides, an illustrative example is provided to support the theoretical results.

Abstract G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-linearity of G-expectation and distribution uncertainty of G-Brownian motion, it is difficult to study this issue. Firstly, the existence of the global unique solution is derived under the linear growth condition and local Lipschitz condition. Secondly, the almost sure exponential stability of the system is analyzed by applying the G-Lyapunov function and G-Itô formula. Finally, an example is introduced to illustrate the stability. The conclusions of this paper can be applied to the stability and risk management of uncertain financial markets.

This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It$ \hat{o} $'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $ (M, N, W) $-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.

This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example.

This paper is concerned with the existence and uniqueness theorems for stochastic functional differential equations with Markovian switching and jump, where the linear growth condition is replaced by more general Khasminskii-type conditions in terms of a pair of Lyapunov-type functions.

This paper investigates finite-time mean square average consensus of second-order multi-agent systems, where connected typologies are directed and subject to Markovian switching, agents dynamics are nonlinear and interrupt by impulses. In order to eliminate the chattering phenomenon in finite-time control, we propose a protocol without sign function, that contains neighborhood and self state feedbacks. Also, by employing graph theory, some graph-related matrices are formed to analyze directed switching topologies. Then, expectations of multi-agent systems energy evolution are bounded in both continuous and discontinuous time by using stochastic and discontinuous stability theories. In this basis, sufficient finite-time mean square consensus criteria are established and their settling times are obtained. Simulation examples prove the theoretical results are correct and the finite-time protocol is valid. [ABSTRACT FROM AUTHOR]

This article aims to design a linear delay feedback control to stabilise an unstable hybrid stochastic delay differential equation in distribution. Under the global Lipschitz condition, sufficient criteria are established to guarantee the stability of the controlled system. Then LMI techniques are employed to design the control law in two structure forms: state feedback and output injection. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stochastic dynamics of a multi‐group stochastic SEIRI epidemic model with logistic population growth, standard incidence rate, and Markovian switching. For this purpose, we first show that the solution of the stochastic system is positive and global. Then we obtain sufficient conditions for the extinction of disease. In addition, the persistence in the mean of disease is proved. Specifically, by constructing suitable stochastic Lyapunov functions, we find a domain that is positive recurrence for the solution of stochastic system. Finally, numerical simulations are employed to verify our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of pth-moment stability of stochastic functional differential equations with Markovian switching and impulsive control via comparison principle. Employing stochastic analysis theory and an impulsive delay differential inequality, we establish a new comparison principle for stochastic functional differential equations with Markovian switching and impulsive control. Using the comparison principle, we derive sufficient conditions for stochastic functional differential equations with Markovian switching and impulsive control by the stability of impulsive delay differential equations. An example is provided to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this article, the quasi-consensus problem of the Markovian switching heterogeneous multi-agent system with cooperative–competitive interactions and parameter uncertainties is investigated. The switch of the agent's dynamics is combined with Markov processes, and the topologies among agents switch between cooperation and competition. Based on graph theory and Lyapunov function theory, the sufficient conditions are given to ensure the quasi-consensus of the Markovian switching multi-agent system. Finally, a numerical simulation is given to illustrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problems on the exponential stability in p-th (p ≥ 2)-moment and the almost sure exponential stability for neutral stochastic differential delay equation with Markovian switching and impulses are analyzed. By establishing an impulsive delay integral inequality, the Lyapunov theorem on the exponential stability in p-th (p ≥ 2)-moment is given. Then, by using the Borel-Cantelli lemma, the almost sure exponential stability theorem is also proved. Two major advantages of these two results are that the differentiability or continuity of the delay function is not required, and that while considering the concerned problem, the difficulty coming from the simultaneous presence of the neutral item, the impulsive disturbance and the stochastic perturbations is overcome. An example is provided to examine the effectiveness and potential of the theoretic results obtained. [ABSTRACT FROM AUTHOR]

A stochastic hybrid population model with Allee effect, Markovian switching and impulsive perturbations is proposed and studied. Sufficient conditions for the extinction and permanence are obtained. Some asymptotic properties are investigated. The lower- and the upper-growth rates of the positive solutions are derived. Numerical simulations are performed to illustrate the main results and to analyze the effects of the Allee effect, the Markovian switching and the impulsive perturbations on the survival and extinction of the population. [ABSTRACT FROM AUTHOR]

The almost sure stability for the stochastic neutral Cohen–Grossberg neural networks (SNCGNNs) with Lévy noise, time‐varying delays, and Markovian switching would be deliberated in this article. By means of the nonnegative semimartingale convergence theorem (NSCT), the neutral Itô formula, M‐matrix method, and selecting appropriate Lyapunov function, several almost sure stability criterions for the SNCGNNs could be derived. Moreover, according to the M‐matrix theory, the upper bounds of the coefficients at any mode are given. Finally, two examples and numerical simulations verify the correctness of theoretical analysis for the stability criterions proposed in the article. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with three noises. The stochastic model studied here includes white noise, telegraph noise and Lévy noise. We established conditions for extinction in probability and in pth moment. We also showed the persistence of disease under different conditions. The presented results are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value function are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find numerical approximation of the value function and optimal strategies. [ABSTRACT FROM AUTHOR]

This article reports on exponential synchronization for stochastic coupled neural networks (NNs) with mixed time‐varying delays, stochastic coupling strength, and Markovian switching. In order to reduce the amount of data transmission and save network resources, an event‐triggered control method is provided in this study. When the triggered condition can be met, the data can be transmitted so that the master and slave systems with limited resources and bandwidth can realize synchronization. By the Lyapunov stability theory and several analysis skills of matrix properties, some new criteria are obtained to make sure that stochastic coupled NNs are mean square exponential stability. These criteria are provided by linear matrix inequalities. Finally, a numerical case further demonstrates the validity of the proposed criteria. [ABSTRACT FROM AUTHOR]

This paper is devoted to moment exponential stability of a class of Markovian switching diffusions with Lévy noise. Our objective is to find verifiable conditions for moment exponential stability and instability. By employing the ireducibility of the Markovian switching process and the Fredholm alternative, we derive explicit criteria for moment exponential stability and instability for linear and general nonlinear systems. Explicit contribution of the Markovian switching to the stability and instability is revealed. Using the criteria developed, we can design feedback controls or perturbations to stabilise a given diffusion with Markovian switching and Lévy noise. Several examples are provided to demonstrate our findings. [ABSTRACT FROM AUTHOR]

The paper is dedicated to studying the problem of existence and uniqueness of solutions as well as existence of and exponential convergence to invariant measures for McKean-Vlasov stochastic differential equations with Markovian switching. Since the coefficients are only locally Lipschitz, we need to truncate them both in space and distribution variables simultaneously to get the global existence of solutions under the Lyapunov condition. Furthermore, if the Lyapunov condition is strengthened, we establish the exponential convergence of solutions' distributions to the unique invariant measure in Wasserstein quasi-distance and total variation distance, respectively. Finally, we give two applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this study, we investigate the stochastic finite-time stability theory and finite-time stabilization of stochastic time-varying nonlinear systems with Markovian switching in the sense of weak solutions. First, we present the stochastic finite-time stability theory under the framework of weak solutions: the existence of weak solutions and stochastic finite-time stability theorems for stochastic time-varying nonlinear systems with Markovian switching. Second, for a class of high-order stochastic nonlinear systems with Markovian switching, a finite-time stabilization controller is constructively designed, and the trivial weak solution of a closed-loop system is proven to be globally finite-time stable in probability. The effectiveness of the proposed finite-time control method is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the Lagrange stability and passivity of a class of discrete-time stochastic Markovian switching neural networks with mixed delays are studied. The mixed delays include time-varying transmission and distribution delays. Global exponential Lagrange stability criterion and passivity criterion in the mean square sense are derived. A numerical example illustrates the usefulness of these criteria. The originality of the proposed method lies in: (i) the criteria are derived directly from the definitions rather than constructing Lyapunov–Krasovskii functional; (ii) the inequalities in the criteria contain only a few decision variables, which is easy to solve and leads to low computational complexity. • Lagrange stability and passivity of discrete-time SM-SNNs with mixed delays are studied. • The time-varying transmission and distribution delays are involved. • Global exponential Lagrange stability criterion and passivity criterion in MMS are derived. • The inequalities in the criteria are easy to solve and lead to low computational complexity. [ABSTRACT FROM AUTHOR]

This paper addresses the exponential stability in mean square of nonlinear stochastic delay differential equations with Markovian switching. Using a novel approach, we present new explicit criteria for exponential stability in mean square. A discussion and two examples are given to illustrate the effectiveness of our criteria. [ABSTRACT FROM AUTHOR]