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Optional sampling of submartingales with scanned index sets

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Abstract

The implication of Doob's optional sampling theorem in general fails to hold for submartingales with partially ordered index sets. Under an additional assumption on the index set (scanning property) we prove optional sampling theorems which are general enough to cover all previous results and, moreover, can be applied for continuous time sampling plans.

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Authors and Affiliations

  1. Institut für Mathematische Statistik der Universität Münster, Einsteinstrasse 62, D-4400, Münster, Germany

    Marion Harenbrock & Norbert Schmitz

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  1. Marion Harenbrock
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  2. Norbert Schmitz
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Harenbrock, M., Schmitz, N. Optional sampling of submartingales with scanned index sets. J Theor Probab 5, 309–326 (1992). https://doi.org/10.1007/BF01046737

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  • DOI: https://doi.org/10.1007/BF01046737

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