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Stopping Time

A stopping time with respect to a filtration (F_t) is a nonnegative extended random variable tau such that

{tau<=t} in F_t

for every t. Thus, the decision whether stopping has occurred by time t depends only on information available by that time, not on future observations. First hitting times of suitably adapted stochastic processes are basic examples.

See also

Filtration, First-Passage Time, Optimal Stopping, Random Variable, Snell Envelope, Stochastic Process

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References

Doob, J. L. Stochastic Processes. New York: Wiley, 1953.Peskir, G. and Shiryaev, A. Optimal Stopping and Free-Boundary Problems. Basel, Switzerland: Birkhäuser, 2006. https://doi.org/10.1007/978-3-7643-7390-0.

Cite this as:

Weisstein, Eric W. "Stopping Time." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StoppingTime.html

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