Definition:Stochastic Process

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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.