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Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 2, Pages 97-119
http://dx.doi.org/10.1155/S1048953303000078

Fractional differential equations driven by Lévy noise

Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, Australia

Received 1 May 2001; Revised 1 January 2003

Copyright © 2003 Hindawi Publishing Corporation. 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

This paper considers a general class of fractional differential equations driven by Lévy noise. The singularity spectrum for these equations is obtained. This result allows to determine the conditions under which the solution is a semimartingale. The prediction formula and a numerical scheme for approximating the sample paths of these equations are given. Almost sure, uniform convergence of the scheme and some numerical results are also provided.