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We study the limiting behavior of fluctuations of synchronized system with small noise around their averaged deterministic limit. There are three regimes depending on how fast the intensity of the noise goes to zero relative to coupling parameter. By simple transformations, the original synchronized system is equivalently converted into the slow–fast system, then we derive the central limit theorem of the slow variable by the martingale method. Therefore, the fluctuation properties corresponding to the original synchronized system are derived. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we prove that for a stochastic differential equation with the coefficients of class C ∞ , the successive approximations of Picard converge in the C ∞ -sense, which implies that the solution to stochastic differential equation is of class C ∞ in the initial value x almost surely. [ABSTRACT FROM AUTHOR]

Abstract: Two bilateral inequalities based on the Borel–Cantelli lemma and a non-negative sequence of bounded random variables were respectively obtained by . However, we observe that the upper bounds in the above cited references are greater than or equal to 1, so the upper bounds of these bilateral inequalities always hold true. In this note, we will extend the lower bound results on the assumptions that the random variables are neither non-negative nor bounded, which could be considered as a version of the Borel–Cantelli lemma with a random weight sequence. As an application, we also discuss the example given in and , and the best result is easily obtained for this example by taking the appropriate weight sequence. [Copyright &y& Elsevier]

Comparison theorems for solutions of one-dimensional backward stochastic differential equations were established by Peng and Cao-Yan, where the coefficients were, respectively, required to be Lipschitz and Dini continuous. In this work, we generalize the comparison theorem to the case where the coefficient is only continuous. [Copyright &y& Elsevier]

Abstract This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study. [ABSTRACT FROM AUTHOR]

Abstract In this paper we prove the stochastic homeomorphism flows for stochastic differential equations (SDEs) with non-Lipschitz coefficients and singular time. [ABSTRACT FROM AUTHOR]