Exact propagator of the Fokker–Planck equation with logarithmic factors in diffusion and drift terms

Abstract

Using the Lie algebraic approach we have derived the exact diffusion propagator of the class of Fokker–Planck equations with logarithmic factors in diffusion and drift terms. The exact diffusion propagator not only enables us to study the time evolution of the corresponding stochastic system, but the knowledge of the propagator can also provide a benchmark for testing approximate numerical or analytical procedures. Furthermore, the Lie algebraic method is very simple and could be easily extended to the more general Fokker–Planck equations with well-defined algebraic structures.