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Generalized fractional kinetic equations: another point of view
Márquez-Carreras David
Source: Adv. in Appl. Probab. Volume 41, Number 3 (2009), 893-910.
Abstract
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.
Primary Subjects: 60G60, 60H15, 60H30
Secondary Subjects: 60G10, 60G15, 60H07
Keywords: Stochastic fractional kinetic and heat equations; Bessel and Riesz potentials; Gaussian processes; Malliavin calculus
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1253281068
Digital Object Identifier: doi:10.1239/aap/1253281068
Zentralblatt MATH identifier:
05625072
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