Soluble models for dynamics driven by a super-diffusive noise

Hongler M-O, Filliger R, Blanchard P. Soluble models for dynamics driven by a super-diffusive noise. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS. 2006;370(2):301-315.We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given. (c) 2006 Elsevier B.V. All rights reserved