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Journal of Applied Mathematics
Volume 2012, Article ID 292740, 16 pages
http://dx.doi.org/10.1155/2012/292740
Research Article

A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Received 17 May 2012; Accepted 12 July 2012

Academic Editor: Yansheng Liu

Copyright © 2012 Wenxue Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stability in probability for some SVIEs is analyzed by the generalized Itô’s formula. Our work shows that the generalized Itô’s formula is powerful and flexible to use in many relevant fields.