TRAJECTORY STATISTICS OF CONFINED LEVY FLIGHTS AND BOLTZMANN-TYPE EQUILIBRIA

摘要

We analyze a specific class of random systems that are driven by a symmetric Levy stable noise, where the Langevin representation is absent. In view of the Levy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) ρ_*(x) ～ exp[-φ(x)]. Here, we infer pdf ρ(x,t) based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for ρ(x, t) and its target pdf ρ_*(x). To simulate the above processes, we construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. We exemplified our algorithm simulating different jump-type processes and discuss the dynamics of real physical systems, where it can be useful.