Moderate Deviation Principle for dynamical systems with small random perturbation

Yutao ma; Ran Wang; Liming Wu

paper

Moderate Deviation Principle for dynamical systems with small random perturbation

arXiv:1107.3432

Abstract

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}Ï(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d $w h er e$ b:\rr^d\to\rr^d $i s$ C^1 $s u c h t ha t$ <x,b(x)> \leq C(1+|x|^2) $,$ Ï:\rr^d\to \MM(d\times n) $i s l oc a l l y L i p sc hi t z ian w i t h l in e a r g r o w t h, an d$ B_t $i s a s t an d a r d B r o w nianm o t i o n t ak in g v a l u es in$ \rr^n $. F r e i d l in - W e n t z e l l^{'} s t h eor e m g i v es t h e l a r g e d e v ia t i o n p r in c i pl e f or$ X^\e $f or s ma l l$ \e$. In this paper we establish its moderate deviation principle.

The result has been published but we didn't know