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Stopping for two-dimensional stochastic processes

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  • Merzbach, Ely

Abstract

The aim of this paper is to introduce some techniques that can be used in the study of stochastic processes which have as parameter set the positive quadrant of the plane R2+. We define stopping lines and derive an interesting property of measurability for them. The notion of predictability is developed, and we show the connection between predictable processes, fields associated with stopping lines, and predictable stopping lines. We also give a theorem of section for predictable sets. Extension to processes indexed by any partially ordered set with some regularity assumptions can be carried out quite easily with the same techniques.

Suggested Citation

  • Merzbach, Ely, 1980. "Stopping for two-dimensional stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 10(1), pages 49-63, June.
    • Handle: RePEc:eee:spapps:v:10:y:1980:i:1:p:49-63
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    Cited by:

    1. Chen, Zongxun, 1997. "On right continuity of a family of two-parameter [sigma]-fields," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 107-113, February.
    2. Diane Saada & Dean Slonowsky, 2006. "A Notion of Stopping Line for Set-Indexed Processes," Journal of Theoretical Probability, Springer, vol. 19(2), pages 397-410, June.

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