Definition:Stochastic Process/Formal Definition
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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.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): stochastic process
- 2016: Jean-François Le Gall: Brownian Motion, Martingales, and Stochastic Calculus ... (previous) ... (next): Definition $1.5$