Abstract

Symmetries of Stochastic Dynamical Systems and Kolmogorov Forward and Backward Equations

G.Unal (Faculty of Sciences, Istanbul Technical University , Maslak, Istanbul, Turkey)

e-mail: gunal@itu.edu.tr

Here, we derive the determining set of PDEs for Ito and Stratonovich dynamical systems without recalling auxiliary theorems. The determining system happens to be a deterministic system of PDEs. We discuss how the symmetries of Ito and Stratonovich dynamical systems are related. We rederive the Kolmogorov forward (Fokker-Planck) and backward equations based on a invariant differential form. Furthermore, we give an explicit formula to obtain solutions of Kolmogorov forwar and backward equations from the symmetries of the stochastic dynamical systems

Section : 12