Printed in the USA c©2003 by North Atlantic Science Publishing Company FRACTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY LÉVY NOISE

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 ap...

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Bibliographic Details
Main Authors: V. V. Anh, R. Mcvinish
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Published: 2001
Subjects:
Key words
Stochastic Fractional Differential Equation
Anomalous Diffusion
Multi- fractality
Long-Range Dependence
Semimartingale Representation
North Atlantic
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.548.6155
http://www.math.ethz.ch/EMIS/journals/HOA/JAMSA/Volume16_2/119.pdf
Description
Summary: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.

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