Biblioteca de la Universidad Complutense de Madrid

The optional sampling theorem for submartingales in the sequentially planned context.

Impacto

Fenoy, Mar y 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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URL Oficial: http://www.sciencedirect.com/science/journal/01677152




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Sampling plan; Sequentially planned; Optional sampling
Materias:Ciencias > Matemáticas > Probabilidades
Código ID:15054
Referencias:

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.

Depositado:03 May 2012 09:36
Última Modificación:06 Feb 2014 10:15

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