KOLMOGOROV FORWARD AND BACKWARD EQUATIONS AND, SYMMETRIES OF STOCHASTIC DYNAMICAL SYSTEMS 



Gazanfer Ünal

Faculty of Science and Letters, Department of Engineering Sciences, Istanbul Technical University, 80626 Maslak, Istanbul, Turkey.



ABSTRACT

       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 forward and backward equations from the symmetries of the stochastic dynamical systems.