Stochastic Theory of Rate Processes

Abstract

This chapter is written under the assumption that the reader has basic knowledge of probability theory such as needed in an elementary course in statistical mechanics, and at least an intuitive feeling for random numbers as those generated by tossing a coin or throwing a die. A random function is a function that assigns a random number to each value of its argument. Using this argument as an ordering parameter, each realization of this function is an ordered sequence of such random numbers. When the ordering parameter is time we have a time series of random variables, which is called a stochastic process. For example, the random function F(t) that assign to each time t the number of cars on a given highway segment is a random function of time, i.e., a stochastic process. Time is a continuous ordering parameter, however if observations of the random function z(t) are made at discrete time 0 < t₁ < t₂,…, < t_n < T, then the sequence z(t_i) is a discrete sample of the continuous function z(t).