Langevin equation with super-heavy-tailed noise

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker–Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorbed, that are equivalent to those for a classical particle in an absorbing medium. The connection between the rate of absorption and the super-heavytailed distribution of the increments is established analytically. A numerical scheme for the simulation of the Langevin equation with super-heavy-tailed noise is developed and used to verify our theoretical results. PACS numbers: 05.40.−a, 05.10.Gg, 02.50.−r (Some figures in this article are in colour only in the electronic version)