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

Backward stochastic partial differential equations driven by infinite dimensional martingales and applications

This paper studies first a result of existence and uniqueness of the solution to a backward stochastic differential equation driven by an infinite dimensional martingale. Then, we apply this result to find a unique solution to a backward stochastic partial differential equation in infinite dimensions. The filtration considered is an arbitrary rightcontinuous filtration, not necessarily the natu...

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

Large Deviation Theory for Stochastic Diierence Equations

The probability density for the solution yn of a stochastic di erence equation is considered. Following Knessl, Matkowsky, Schuss, and Tier [1] it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large deviation results for a sum of independent identically distributed random variables and for the joi...

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...