Definition:Stochastic Process

Definition

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.

Also known as

A stochastic process is also known as a random process.

Also see

• Results about stochastic processes can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): stochastic process
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): stochastic process