Mellin transform and subordination laws in fractional diffusion processes

Details Mellin transform and subordination laws in fractional diffusion processes Mellin transform and subordination laws in fractional diffusion processes

2007-02-06

arxiv.org/abs/math/0702133v1

Fractional Calculus and Applied Analysis, Vol. 6 No 4 (2003), pp. 441-459

Mathematics

Probability

21 pages

Scientific paper

The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more generally the probability distributions governed by generalized diffusion equations of fractional order in space and/or in time. In these cases the related stochastic processes are self-similar and are simply referred to as fractional diffusion processes. We provide some integral formulas involving the distributions of these processes that can be interpreted in terms of subordination laws.

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