Dynamic models of long-memory processes driven by Lévy noise

V. V. Anh; C. C. Heyde; N. N. Leonenko

doi:10.1239/jap/1037816015

Dynamic models of long-memory processes driven by Lévy noise

V. V. Anh^*, C. C. Heyde, N. N. Leonenko

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

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.

Original language	English
Pages (from-to)	730-747
Number of pages	18
Journal	Journal of Applied Probability
Volume	39
Issue number	4
DOIs	https://doi.org/10.1239/jap/1037816015
Publication status	Published - Dec 2002

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title = "Dynamic models of long-memory processes driven by L{\'e}vy noise",

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 L{\'e}vy 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.",

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AU - Heyde, C. C.

AU - Leonenko, N. N.

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N2 - 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.

AB - 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.

KW - Fractional stochastic differential equations

KW - Heavy-tailed processes

KW - Long-range dependence

KW - Lévy processes

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DO - 10.1239/jap/1037816015

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JO - Journal of Applied Probability

JF - Journal of Applied Probability

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Dynamic models of long-memory processes driven by Lévy noise

Abstract

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