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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, 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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