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Advances in Mathematical Physics
Volume 2014, Article ID 307819, 10 pages
http://dx.doi.org/10.1155/2014/307819
Research Article

A Weak Convergence to Hermite Process by Martingale Differences

Department of Mathematics and Physics, Bengbu College, 1866 Caoshan Road, Bengbu, Anhui 233030, China

Received 5 May 2014; Accepted 25 June 2014; Published 14 July 2014

Academic Editor: Carlo Cattani

Copyright © 2014 Xichao Sun and Ronglong Cheng. 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

We consider the weak convergence to general Hermite process of order with index . By applying martingale differences we construct a sequence of multiple Wiener-Itô stochastic integrals such that it converges in distribution to the Hermite process .