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Stopping and set-indexed local martingales

Author

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  • Ivanoff, B. Gail
  • Merzbach, Ely

Abstract

Set-indexed local martingales are defined and studied. We present some optional sampling theorems for strong martingales, martingales and weak martingales. The class of set-indexed processes which are locally of class (D) is introduced. A Doob-Meyer decomposition is obtained: any local weak submartingale has a unique decomposition into the sum of a local weak martingale and a local predictable increasing process. Finally some examples are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:83-98
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Balan, R. M., 2001. "A strong Markov property for set-indexed processes," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 219-226, June.
    2. Dean Slonowsky, 2001. "Strong Martingales: Their Decompositions and Quadratic Variation," Journal of Theoretical Probability, Springer, vol. 14(3), pages 609-638, July.
    3. 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.
    4. Cassese, Gianluca, 2010. "Supermartingale decomposition with a general index set," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1060-1073, July.

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