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Dynamic models of long-memory processes driven by Lévy noise

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

V. V. Anh ,
C. C. Heyde  and
N. N. Leonenko
V. V. Anh*
Affiliation:
Queensland University of Technology
C. C. Heyde*
Affiliation:
Australian National University
N. N. Leonenko*
Affiliation:
Cardiff University
*
∗ Postal address: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, Australia. Email address: v.anh@qut.edu.au
∗∗ Postal address: School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia.
∗∗∗ Postal address: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK.
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Abstract

A class of continuous-time models is developed for modelling data with heavy tails and long-range dependence. These models are based on the Green function solutions of fractional differential equations driven by Lévy noise. Some exact results on the second- and higher-order characteristics of the equations are obtained. Applications to stochastic volatility of asset prices and macroeconomics are provided.

Keywords

Long-range dependenceLévy processesheavy-tailed processesfractional stochastic differential equations

MSC classification

Primary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 730 - 747
Copyright
Copyright © Applied Probability Trust 2002 

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