What Is a Stochastic Process

This chapter provides the mathematical framework and example illustrations of stochastic processes as families of random variables with values in some measurable (state) space S, such as the integers or the real line or higher dimensional Euclidean space, and indexed by some set Λ. Examples include i.i.d. sequences, random walks, Brownian motion, Poisson processes, branching processes, queue processes, Markov processes, and various martingale processes. Special emphasis is given to existence and constructions of these important classes of stochastic processes.