Stochastic Process

A stochastic process is a family of Random Variables $\{x(t,\bullet), t\in{\mathcal J}\}$ from some Probability Space $(S, \Bbb{S}, P)$ into a State Space $(S', \Bbb{S}')$. Here, ${\mathcal J}$ is the Index Set of the process.

See also Index Set, Probability Space, Random Variable, State Space

References

Doob, J. L. ``The Development of Rigor in Mathematical Probability (1900-1950).'' Amer. Math. Monthly 103, 586-595, 1996.