Electronic Journal of Probability

Pseudo-Processes Governed by Higher-Order Fractional Differential Equations

Luisa Beghin

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Abstract

We study here a heat-type differential equation of order $n$ greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess $\Psi _{n}$ (coinciding with the one governed by the standard, non-fractional, equation) with a time argument $\mathcal{T}_{\alpha }$ which is itself random. The distribution of $\mathcal{T}_{\alpha }$ is presented together with some features of the solution (such as analytic expressions for its moments.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 16, 467-485.

Dates
Accepted: 31 March 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819089

Digital Object Identifier
doi:10.1214/EJP.v13-496

Mathematical Reviews number (MathSciNet)
MR2386739

Zentralblatt MATH identifier
1191.60039

Subjects
Primary: 60G07: General theory of processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Keywords
Higher-order heat-type equations Fractional derivatives Wright functions Stable laws

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Beghin, Luisa. Pseudo-Processes Governed by Higher-Order Fractional Differential Equations. Electron. J. Probab. 13 (2008), paper no. 16, 467--485. doi:10.1214/EJP.v13-496. https://projecteuclid.org/euclid.ejp/1464819089


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