Stochastic Calculus and Some Models of Irreversible Processes

Each type, It()' s or Stratonovich' s, of the stochastic differential equations (SDE) has its own role to play in the theory of irreversible processes. It is argued generally that colored-noise random forces in mechanical equations of motion should, in the white noise limit, be interpreted in the sense of the Stratonovich type SDE. Its transformation into the It8 type facilitates the study of ensemble averages. By way of illustration, the problems of the random frequency modulation and the Brownian motion of a spin are treated to show how straightforwardly the SDE can bring out basic features of the irreversible processes.