Volume no :6, Issue no: 2, December (2010)

Journal of Mathematical Sciences: Advances and Applications

THE STOCHASTIC INTEGRAL WITH RESPECT TO THE SUB-FRACTIONAL BROWNIAN MOTION WITH

Author's: Guangjun Shena and Litan Yan
Pages: [219] - [239]
Received Date: October 27, 2010
Submitted by:

Abstract

We develop a stochastic calculus for the sub-fractional Brownian motion with index by using the techniques of the Malliavin calculus. We establish estimates in maximal inequalities for the divergence integral with respect to sub-fractional Brownian motion. We also study the variation of the divergence integral and generalize the result of sub-fractional Brownian motion for this divergence integral.

Keywords

sub-fractional Brownian motion, Malliavin calculus, divergence integral, p-variation.