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A Characterization of Stopping Times
Frank B. Knight and Bernard Maisonneuve
The Annals of Probability
Vol. 22, No. 3 (Jul., 1994), pp. 1600-1606
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2245036
Page Count: 7
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Let R be a random time in F∞, the terminal element of a filtration Ft satisfying the usual hypotheses. It is shown that if optimal sampling holds at R for all bounded martingales, then R is optional. If Ft is the natural pseudo-path filtration of a measurable process Xt, then R is optional if (and only if) the conditional distribution of XR + . given FR is ZR, where Zt is an optional version of the conditional distribution of Xt +. given Ft.
The Annals of Probability © 1994 Institute of Mathematical Statistics