Some properties of the Ito-Wiener expansion of the solution of a stochastic differential equation and local times

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Rudenko, Alexey

关键词: Ito-Wiener expansion;    Stochastic differential equation;    Local time;    Renormalized local time;    Second quantization operator;   

DOI  :  10.1016/j.spa.2012.03.009

来源: Elsevier

【 摘 要 】

In this paper, we use the formula for the Ito-Wiener expansion of the solution of the stochastic differential equation proven by Krylov and Veretennikov to obtain several results concerning some properties of this expansion. Our main goal is to study the Ito-Wiener expansion of the local time at the fixed point for the solution of the stochastic differential equation in the multidimensional case (when standard local time does not exist even for Brownian motion). We show that under some conditions the renormalized local time exists in the functional space defined by the L-2-norm of the action of some smoothing operator. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free