an:06781667
Zbl 1371.60080
??aba, Mariusz; Garbaczewski, Piotr; Stephanovich, Vladimir
Trajectory statistics of confined L??vy flights and Boltzmann-type equilibria
EN
Acta Phys. Pol. B 44, No. 5, 1109-1122 (2013).
00370344
2013
j
60G51 82C31
Summary: We analyze a specific class of random systems that are driven by a symmetric L??vy stable noise, where the Langevin representation is absent. In view of the L??vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) \(\rho_*(x)\sim\exp[-\Phi(x)]\). Here, we infer pdf \(\rho(x,t)\) 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 \(\rho(x,t)\) and its target pdf \(\rho_*(x)\). 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.