Overview of Stochastic Processes
Oliver C. Ibe · 2011
Stochastic processes deal with the dynamics of probability theory. The concept of stochastic processes enlarges the random variable concept to include time. A random process {X (t)|t⩾0} is called a counting process if X (t) represents the total number of “events” that have occurred in the interval [0, t). A counting process is defined to be an independent increment process if the number of events that occur in disjoint time intervals is an independent random variable. The chapter also describes the stationary increment process, Poisson processes, renewal process, Markov processes, and the Gaussian processes. Controlled Vocabulary Terms Gaussian process; Markov process; Poisson process; probability theory; random variables; renewal theory; stochastic processes