Introduction to Stochastic Processes

Abstract

Classical mechanics usually ascribes a deterministic time evolution to the dynamic variables of a system. When this is not the case we can, in many cases, give probability distributions for the values of the variables, which, together with an ensemble interpretation of the probability, forms the basis for statistical methods in physics. When the time evolution of these distribution functions is known, the resulting structure is called a stochastic process. There is a vast mathematical literature on this field, and its importance for physics has grown continuously. The classical physical material can be found in Wax (1954).