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arXiv · 0909.3385

Convergence of a kinetic equation to a fractional diffusion equation

Giada Basile·Anton Bovier
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Abstract

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), Y(t)), where K(t) is a autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, while Y(t) is an additive functional of K(t). We prove that under a suitable rescaling the process Y converges in distribution to a Levy process, stable with index 3/2. Moreover, the solution of the linear Boltzmann equation converges to the solution of a fractional diffusion equation.

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Giada Basile, Anton Bovier. 2009-09-18. Convergence of a kinetic equation to a fractional diffusion equation. https://arxiv.org/abs/0909.3385

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