Category:Definitions/Stochastic Processes

This category contains definitions related to Stochastic Processes.
Related results can be found in Category:Stochastic Processes.

Informal Definition

A stochastic process is a sequence of random variables representing the evolution of some real-world physical process over time.

Formal Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\struct {E, \EE}$ be a measurable space.

Let $I$ be a set.

Let $\family {X_i}_{i \mathop \in I}$ be a $I$-indexed family of $E$-valued random variables.

We call $\family {X_i}_{i \mathop \in I}$ a stochastic process.