Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite dimensional semimartingales
نویسنده
چکیده
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 is a separable reflexive Banach space with Schauder basis, a simplified expression of the rate function for the stochastic integral {Xn− · Yn} has been given in terms of the rate function for {(Xn, Yn)}. Similar result for stochastic differential equation has also been proved. MSC 2000 subject classifications: 60H05, 60H10 , 60H20, 60F10
منابع مشابه
Stochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کاملWong-Zakai type convergence in infinite dimensions
The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite-dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finit...
متن کاملExistence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
متن کامل
Large Deviations for the Shell Model of Turbulence Perturbed by Lévy Noise
The large deviations theory is among the most classical areas in probability theory with many deep developments and applications. Several authors have established the Wentzell-Freidlin type large deviation estimates for a class of infinite dimensional stochastic differential equations (see for eg., Budhiraja and Dupuis [9], Da Prato and Zabczyk [12], Kallianpur and Xiong [20]). In these works t...
متن کاملNumerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کامل