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Generalized fractional kinetic equations: another point of view

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

David Márquez-Carreras
David Márquez-Carreras*
Affiliation:
Universitat de Barcelona
*
∗ Postal address: Departament de Probabilitat, Lògica i Estadística, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain. Email address: davidmarquez@ub.edu
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Abstract

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In this paper we deal with generalized fractional kinetic equations driven by a Gaussian noise, white in time and correlated in space, and where the diffusion operator is the composition of the Bessel and Riesz potentials for any fractional parameters. We give results on the existence and uniqueness of solutions by means of a weak formulation and study the Hölder continuity. Moreover, we prove the existence of a smooth density associated to the solution process and study the asymptotics of this density. Finally, when the diffusion coefficient is constant, we look for its Gaussian index.

Keywords

Stochastic fractional kinetic and heat equationsBessel and Riesz potentialsGaussian processesMalliavin calculus

MSC classification

Primary: 60G60: Random fields 60H15: Stochastic partial differential equations 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60G10: Stationary processes 60G15: Gaussian processes 60H07: Stochastic calculus of variations and the Malliavin calculus
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 3 , September 2009 , pp. 893 - 910
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Partially supported by the grant MTM 2006-01351.

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