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Stochastic Process

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the index set of the process.

Papoulis (1984, p. 312) describes a stochastic process x(t) as a family of functions.

See also

Index Set, Probability Space, Random Variable, State Space

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References

Doob, J. L. "The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103, 586-595, 1996.Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.Ross, S. M. Stochastic Processes, 2nd ed. New York: Wiley, p. 59, 1996.

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Stochastic Process

Cite this as:

Weisstein, Eric W. "Stochastic Process." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StochasticProcess.html

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