Journal of Applied Probability

Dynamic models of long-memory processes driven by Lévy noise

V. V. Anh, C. C. Heyde, and N. N. Leonenko

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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.

Article information

Source
J. Appl. Probab. Volume 39, Number 4 (2002), 730-747.

Dates
First available: 20 November 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1037816015

Digital Object Identifier
doi:10.1239/jap/1037816015

Mathematical Reviews number (MathSciNet)
MR1938167

Zentralblatt MATH identifier
1016.60039

Subjects
Primary: 60G10: Stationary processes
Secondary: 60M20

Keywords
Long-range dependence Lévy processes heavy-tailed processes fractional stochastic differential equations

Citation

Anh, V. V.; Heyde, C. C.; Leonenko, N. N. Dynamic models of long-memory processes driven by Lévy noise. Journal of Applied Probability 39 (2002), no. 4, 730--747. doi:10.1239/jap/1037816015. http://projecteuclid.org/euclid.jap/1037816015.


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