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The optional sampling theorem for submartingales in the sequentially planned context

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  • Fenoy, M. Mar
  • Ibarrola, Pilar

Abstract

The optional sampling theorem is considered in the sequentially planned context. We prove the optional sampling theorem for direct successors and for sampling plans with a finite number of stages. Also, the theorem is studied in the general case under a uniform integrability condition; we obtain it for submartingales with a last element, and for submartingales that verify a bounded condition based on uniform integrability.

Suggested Citation

  • Fenoy, M. Mar & Ibarrola, Pilar, 2007. "The optional sampling theorem for submartingales in the sequentially planned context," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 826-831, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:826-831
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    1. M. Mar Fenoy & Pilar Ibarrola, 2003. "Sufficiency in sequentially planned decision procedures," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 365-384, December.
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