Basic Concepts

Abstract

Consider a family of random variables ${X}_{t}$ defined on a common probability space $(\Omega, \mathcal{F},\mathrm{P})$ and indexed by a parameter $t \in T$. If the parameter set T is a subset of the real line (most commonly $\mathbb{Z}$, ${\mathbb{Z}}^{+}$, $\mathbb{R}$, or ${\mathbb{R}}^{+}$), we refer to the parameter t as time, and to ${X}_{t}$ as a random process. If T is a subset of a multi-dimensional space, then X _t called a random field.