Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
Mariusz Żaba,
Piotr Garbaczewski,
Vladimir Stephanovich
Abstract:We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function ρ(x, t). Our main goal is to demonstrate a compatibility of a direct solution method (an explicit, albeit numerically assisted, integration of the master equation) with an indirect path-wise procedure, recently proposed in [Physica A 392, 3485, (201… Show more
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