In this article we address the stability of linear stochastic differential equations. particular, focus our attention on non-normality in Following Higham and Mao study a test problem for non-normal equations, that is stable without noise, prove property conjectured by Mao, an exponentially small (in dimension) noise term able to destabilise mean-square sense solution SDE.

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include correspondence weak solutions equations, well-posedness, regularity estimates, exponential ergodicity, long time large d...

For system identification, the ordinary differential equations (ODEs) model is popular for its accuracy and effectiveness. Consequently, the ODEs model is extended to the stochastic differential equations (SDEs) model to tackle the stochastic case intuitively. But the existence of stochastic integral is a rigid barrier. We simply transform the SDEs to their corresponding stochastic difference e...

In this article, we summarize some results on the existence and qualitative behavior of stochastic dynamical systems in infinite dimensions. The three main examples covered are stochastic systems with finite memory (stochastic functional differential equations-sfde’s), semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s). Due to limitations of...

The main aim of this paper is to investigate the exponential stability of stochastic functional differential equations with Markovian switching. The Razumikhin argument and the generalized Itô formula will play their important roles in this paper. Applying our new results to several important types of equations e.g. stochastic differential delay equations and stochastic differential equations, ...