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Fractional kinetic equations driven by Gaussian or infinitely divisible noise

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

J. M. Angulo ,
V. V. Anh ,
R. McVinish  and
M. D. Ruiz-Medina
J. M. Angulo*
Affiliation:
University of Granada
V. V. Anh*
Affiliation:
Queensland University of Technology
R. McVinish*
Affiliation:
Queensland University of Technology
M. D. Ruiz-Medina*
Affiliation:
University of Granada
*
∗ Postal address: Department of Statistics and Operations Research, University of Granada, Campus Fuente Nueva s/n, E-18071 Granada, Spain.
∗∗∗ Postal address: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
∗∗∗ Postal address: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
∗ Postal address: Department of Statistics and Operations Research, University of Granada, Campus Fuente Nueva s/n, E-18071 Granada, Spain.
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Abstract

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In this paper, we consider a certain type of space- and time-fractional kinetic equation with Gaussian or infinitely divisible noise input. The solutions to the equation are provided in the cases of both bounded and unbounded domains, in conjunction with bounds for the variances of the increments. The role of each of the parameters in the equation is investigated with respect to second- and higher-order properties. In particular, it is shown that long-range dependence may arise in the temporal solution under certain conditions on the spatial operators.

Keywords

Fractional diffusionfractional heat equationfractional kinetic equationlong-range dependence

MSC classification

Primary: 60G60: Random fields
Secondary: 60J60: Diffusion processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 366 - 392
Copyright
Copyright © Applied Probability Trust 2005 

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