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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
Stable URL: http://www.jstor.org/stable/2245036
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Characterization of Stopping Times
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Abstract

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.

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