[PDF] Top 20 A note on exponential almost sure stability of stochastic differential equation

... the exponential almost sure stability of a certain class of stochastic differential ...the almost sure stability, replacing Lipschitz continuity and linear ... See full document

... the stability or synchronization criteria for NNs involving diffusion and time-varying delays are found in ...Moreover, note that many systems such as biological networks and man-made NNs are described by ... See full document

... about almost sure stabil- ity of Runge-Kutta type methods for SDDEs, and nearly all existing results concerned with Euler-Maruyama type ...the almost sure stability of the S-ROCK method ... See full document

... scalar differential equation x(t) = ˙ αx(t) is unstable when α > 0 but it can be stabilized by a Brownian ...linear stochastic differential equation ... See full document

... Pantograph differential equation was used by Ock- endon and Tayler [15] to investigate how the electric current is collected by the pantograph of an electric locomotive, from where it gets the ...tograph ... See full document

... of differential equations by noise have been studied by many authors and we here mention Arnold, Crauel & Wihstutz (1983); Pardoux & Wihstutz (1992); Mao (1994); Kwieci´ nska (2002); Ap- pleby & Mao ... See full document

... the almost sure stability of SDEs with the global Lipschitz coefficients, but the requirements on the time stepsize are very ...nonlinear equation system at each ... See full document

... hybrid stochastic retarded systems (HSRSs) have been widely used since stochastic modelling plays an important role in many branches of science and ...Consequently, stability analysis of HSRSs and ... See full document

... a stochastic delay differential equation driven by a fractional Brow- nian motion with Hurst parameter H > ...for stochastic delay differential equations with hereditary drift driven by a fractional ... See full document

... special stochastic delay systems, stochastic pantograph equations (SPEs) with unbounded delay have been investigated by many scholars, we can refer to Baker and Buck- war [3], Appleby and Buckwar [2], Fan ... See full document

... of exponential stability of neutral stochastic functional differential equations, and in this paper, we shall further our study in this ...neutral stochastic functional ... See full document

... By Ito’s formula and the delay term of the equation, we give the proof of Theorem 3.1. The highlight of the proof is that we give the mean square boundedness of the solution to the equation by dividing the ... See full document

... discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential ...guarantee exponential stability of the so- ...the equation ... See full document

... pantograph stochastic differential equations(PSDEs) are special SDDEs that have unbounded delays (see ...On stability of a PSDE, [1] investigated the growth and decay rates of special scalar PSDEs, ... See full document

... of stochastic partial different equations in a separable Hilbert space has become an important area of investigation in the past two decades because of their applications to various problems arising in physics, ... See full document

... By Ito’s formula and the delay term of the equation, we give the proof of Theorem .. The highlight of the proof is that we give the mean square boundedness of the solution to the equation by dividing the ... See full document

... of stochastic system model, and their stability analysis has attracted considerable attention in recent ...most stochastic systems cannot be solved explicitly, the research on stochastic ... See full document

... for stochastic differential equations (SDEs) has recently received a more and more ...attention. Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated ... See full document

... = f(x(t), x(t − τ ), t, r(t)) + g (x(t), x(t − τ ), t, r(t))dB(t). (1.3) In [12], the existence and uniqueness of the solution to Eq. (1.3) are discussed and, moreover, both moment asymptotic boundedness and moment ... See full document

... The content of this paper is arranged as follows. In Section 2, some necessary definitions, notations, and lemmas used in this paper will be introduced. In Section 3, by establishing a lemma, some sufficient conditions ... See full document