Pseudoprocesses governed by higher-order fractional differential equations

Details Pseudoprocesses governed by higher-order fractional differential equations Pseudoprocesses governed by higher-order fractional differential equations

2007-05-24

arxiv.org/abs/0705.3598v1

Electronic Journal of Probability, Vol.15 (2010), n.22, 684-709

Mathematics

Probability

Submitted for publication (March 2007)

Scientific paper

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 (coinciding with the one governed by the standard, non-fractional, equation) with a time argument T which is itself random. The distribution of T is presented together with some features of the solution (such as analytic expressions for its moments).

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