Pseudoprocesses governed by higher-order fractional differential equations
Probability
2011-03-03 v1
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 (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).
Cite
@article{arxiv.0705.3598,
title = {Pseudoprocesses governed by higher-order fractional differential equations},
author = {Luisa Beghin},
journal= {arXiv preprint arXiv:0705.3598},
year = {2011}
}