Fenoy, Mar and Ibarrola Muñoz, Pilar
(2007)
*The optional sampling theorem for submartingales in the sequentially planned context.*
Statistics & Probability Letters, 77
(8).
pp. 826-831.
ISSN 0167-7152

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Official URL: http://www.sciencedirect.com/science/journal/01677152

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Sampling plan; Sequentially planned; Optional sampling |

Subjects: | Sciences > Mathematics > Probabilities |

ID Code: | 15054 |

References: | Bochner, S., 1955. Partial ordering in the theory of martingales. Ann. Math. 1 (62). Chow, Y., Robbins, H., Siegmund, D., 1971. Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston. Doob, J., 1953. Stochastic Processes. Wiley, New York. Fenoy, M., Ibarrola, P., 2003. Sufficiency in sequentially planned decision procedures. Test 12 (2), 365–384. Helms, L., 1958. Mean convergence of martingales. Trans. Amer. Math. Soc. (87) 439–446. Krickeberg, K., 1956. Convergence of martingales with a directed indexed set. Trans. Amer. Math. Soc. (83) 313–337. Schmitz, N., 1993. Optimal Sequentially Planned Decision Procedures, Lectures Notes in Statistics. Springer, New York. Washburn, R., Willsky, A., 1981. Optional sampling of submartingales indexed by partially ordered sets. Ann. Probab. 9 (6), 957–970. |

Deposited On: | 03 May 2012 09:36 |

Last Modified: | 06 Feb 2014 10:15 |

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