Electronic Journal of Probability

Pseudo-Processes Governed by Higher-Order Fractional Differential Equations

Luisa Beghin

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

This work is licensed under aCreative Commons Attribution 3.0 License.


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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