Dynamic theory of stochastic movement of systems

Abstract

The author studies the dynamic theory of stochastic processes. The dynamic theory concerns an evolution equation which contains a potential function , and the diffusion matrix and drift vector. The case with no potential term can be treated in the framework of the conventional theory of Markov processes of Kolmogorov and Itˆo, which is a kinematic theory. The kinematic equation determines Markov (diffusion) processes, i.e.,the movement of systems. By contrast, the author considers the equation of motion in the mechanics part of the Show more