Stochastic is synonymous with "random." The word is of Greek origin and means "pertaining to chance" (Parzen 1962, p. 7). It is used to indicate that a particular subject is seen from point of view of randomness. Stochastic is often used as counterpart of the word "deterministic," which means that random phenomena are not involved. Therefore, stochastic models are based on random trials, while deterministic models always produce the same output for a given starting condition.

# Stochastic

## See also

Deterministic, Random, Random Variable, Stochastic Approximation, Stochastic Calculus, Stochastic Geometry, Stochastic Group, Stochastic Matrix, Stochastic Optimization, Stochastic Process, Stochastic Resonance
*This entry contributed by Vincenzo
Origlio*

## Explore with Wolfram|Alpha

## References

Doob, J. L.*Stochastic Processes.*New York: Wiley, p. 46, 1953.Gnedenko, B. V. and Khinchin, A. Ya.

*An Elementary Introduction to the Theory of Probability.*New York: Dover, pp. 60 and 121, 1962.Lawler, G. F.

*Introduction to Stochastic Processes.*Boca Raton, FL: Chapman & Hall/CRC, p. 1, 1995.Neelamkavil, F.

*Computer Simulation and Modelling.*New York: Wiley, p. 4, 1987.Parzen, E.

*Stochastic Processes.*Oakland CA: Holden Day, p. 7, 1962.Wolfram, S.

*A New Kind of Science.*Champaign, IL: Wolfram Media, pp. 588 and 968, 2002.

## Referenced on Wolfram|Alpha

Stochastic## Cite this as:

Origlio, Vincenzo. "Stochastic." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/Stochastic.html