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

L. Beghin and E. Orsingher

Stochastic Processes and their Applications, 2005, vol. 115, issue 6, 1017-1040

Abstract: We prove that the pseudoprocesses governed by heat-type equations of order n[greater-or-equal, slanted]2 have a local time in zero (denoted by ) whose distribution coincides with the folded fundamental solution of a fractional diffusion equation of order 2(n-1)/n, n[greater-or-equal, slanted]2. The distribution of 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 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.

Keywords: Heat-type; equation; Fractional; diffusion; equations; Local; time; Feynman-Kac; functional; Wright; functions; Stable; laws; Vandermonde; determinant; Mittag-Leffler; functions (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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