Search

In this paper, we have studied stochastic differential equations with unbounded delay in fractional power spaces perturbed by fractional Ornstein–Uhlenbeck process Y H , ξ ⁢ (t) with H ∈ (1 2 , 1) . Subsequently, the existence and uniqueness of mild solution of the considered equation have been proved with fixed-point theorem. Finally, we obtain the global attracting set of the considered equations by some stochastic analysis and inequality technique. [ABSTRACT FROM AUTHOR]

Based on the Girsanov theorem for a kind of Volterra-Gaussian process, which are the generalization of fractional Brownian motion, Liouville fractional Brownian motion, and fractional Ornstein-Uhlenbeck process, we establish the Harnack inequalities for a class of stochastic functional differential equations driven by a kind of Volterra-Gaussian processes with a subordinator by an approximation technique. Some known results have been generalized and improved. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of coupled neutral stochastic partial differential equations driven by fractional Brownian motion with Hurst parameter H ∈ (0 , 1 / 2) ∪ (1 / 2 , 1). On account of the Perov's fixed point theorem and semigroup theory, we prove the existence and uniqueness of mild solution. Subsequently, by using delay integral inequalities, we identify the global attracting sets of the equations under investigation. Furthermore, we obtain some sufficient conditions that ensure the exponential decay of mild solutions in the pth moment. Lastly, we present an example to illustrate our theory in this work. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the controllability for a class of neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter in a Hilbert space. By using the stochastic analysis of fractional Brown motion with Hurst parameter , the properties of operator semigroup and the Banach fixed point theorem, the sufficient conditions for the controllability of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

We are concerned with a class of neutral stochastic functional differential equations driven by fractional Brownian motion (fBm) in the Hilbert space. We obtain the global attracting sets of this kind of equations driven by fBm with Hurst parameter ћ ∈ (0, 1/2). Especially, some sufficient conditions which ensure the exponential decay in the p-th moment of the mild solution of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of stochastic fractional evolution equations with infinite delay and a fractional Brownian motion in a Hilbert space. By the stochastic analysis technique, we establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz condition with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of Poisson Stepanov-like almost automorphy (or PoissonS2-almost automorphy). Under some suitable conditions on the coefficients, we establish the existence and uniqueness of Stepanov-like almost automorphic mild solution to a class of semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solution. Finally, we give an example to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM PUBLISHER]