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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 479873, 10 pages
http://dx.doi.org/10.1155/2014/479873
Research Article

Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise

1Department of Mathematics and Physics, Bengbu College, 1866 Caoshan Road, Bengbu, Anhui 233030, China
2School of Mathematics and Statistics, Nanjing Audit University, 86 West Yu Shan Road, Pukou, Nanjing 211815, China

Received 21 September 2013; Revised 27 December 2013; Accepted 27 December 2013; Published 12 February 2014

Academic Editor: Ming Li

Copyright © 2014 Xichao Sun and Junfeng Liu. 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 a class of stochastic fractional equations driven by fractional noise on , with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise.