# Stochastic Processes

• Eugene Wong
Part of the Springer Texts in Electrical Engineering book series (STELE)

## Abstract

Usage of the term “stochastic process” is not entirely standard. The sense in which we shall use it is probably the most conventional. A stochastic process {Xt, t ∈ T} is a family of random variables defined on a single probability space (Ω,A,P) and indexed by points t in a subset T of the real line. Although it is not necessary to do so, we shall usually associate the parameter t with time. The set T is called the parameter space of the process. If T is a countable set, say T={t1, t2, ...}, then the process {Xt, t ∈ T} is nothing more than a sequence, which was discussed in Chapter 3. We shall be more interested in situations where T is an interval, the most common cases being T = [0, 1], [0, ∞), and (-∞, ∞). If T is an interval, we call the process a continuous parameter process. Unless otherwise stated, we always assume that T is an interval.

## Keywords

Brownian Motion Markov Process Covariance Function Gaussian Process Sample Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.