On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales

Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite dimensional semimartingales

Let H be a separable Banach space. We considered the sequence of stochastic integrals {Xn− · Yn} where {Yn} is a sequence of infinite dimesnional H semimartingales and Xn are H valued cadlag processes. Assuming that {(Xn, Yn)} satisfies large deviation principle, a uniform exponential tightness condition is described under which large deviation principle holds for {(Xn, Yn, Xn− · Yn)}. When H i...

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Approximate Solutions of Set-Valued Stochastic Differential Equations

In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state th...

Exponential Stability for Stochastic Differential Equations with Respect to Semimartingales

Consider a stochastic differential equation with respect to semimartingales dX(t)=AX(f)dp(t)+G(X(t),r)dM(r) which might be regarded as a stochastic perturbed system of dX(t)=AX(t)d/L(t). Suppose the second equation is exponentially stable almost surely. What we are interested in in this paper is to discuss the sufficient conditions under which the first equation is still exponentially stable al...