The distribution of the local time for pseudoprocesses and its connection with fractional diffusion equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Beghin, L ; Orsingher, E

关键词: heat-type equation;    fractional diffusion equations;    local time;    Feynman-Kac functional;    Wright functions;    stable laws;    Vandermonde determinant;    Mittag-Leffler functions;   

DOI  :  10.1016/j.spa.2005.02.001

来源: Elsevier

【 摘 要 】

We prove that the pseudoprocesses governed by heat-type equations of order n >= 2 have a local time in zero (denoted by L-0(n)(t)) whose distribution coincides with the folded fundamental solution of a fractional diffusion equation of order 2(n - 1)1n, n >= 2. The distribution of L-0(n)(t) is also expressed in terms of stable laws of order n/(n - 1) and their form is analyzed. Furthermore, it is proved that the distribution of L-0(n)(t) is connected with a wave equation as n -> infinity. The distribution of the local time in zero for the pseudoprocess related to the Myiamoto's equation is also derived and examined together with the corresponding telegraph-type fractional equation. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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