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The past of a stopping point and stopping for two-parameter processes

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  • Fouque, Jean-Pierre

Abstract

Optional increasing paths passing through a given stopping point are studied. A characterization of the two extreme optional increasing paths is obtained. The past of a stopping point is defined, and a description of the largest stopping point smaller than two given stopping points is given. A stopping procedure is naturally associated with this notion of infimum. Stopped martingales and stopped filtrations are studied. "Local martingales" are defined and studied along horizontal and vertical lines. A nontrivial example of "local martingale" is given.

Suggested Citation

  • Fouque, Jean-Pierre, 1983. "The past of a stopping point and stopping for two-parameter processes," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 561-577, December.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:4:p:561-577
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    Cited by:

    1. Ivanoff, B. Gail & Merzbach, Ely, 1995. "Stopping and set-indexed local martingales," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 83-98, May.

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