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Supermartingale decomposition with a general index set

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  • Cassese, Gianluca

Abstract

We prove results on the existence of Doléans-Dade measures and of the Doob-Meyer decomposition for supermartingales indexed by a general index set.

Suggested Citation

  • Cassese, Gianluca, 2010. "Supermartingale decomposition with a general index set," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1060-1073, July.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1060-1073
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    References listed on IDEAS

    as
    1. Yosef, Arthur, 2009. "Set indexed strong martingales and path independent variation," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1083-1088, April.
    2. Cassese, Gianluca, 2007. "Decomposition of supermartingales indexed by a linearly ordered set," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 795-802, April.
    3. Ivanoff, B. Gail & Sawyer, P., 2003. "Local time for processes indexed by a partially ordered set," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 1-15, January.
    4. 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.
    5. De Giosa, Marcello & Mininni, Rosamaria, 1995. "On the Doléans function of set-indexed submartingales," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 71-75, July.
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