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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 3, Pages 563–568
DOI: https://doi.org/10.4213/tvp3902 (Mi tvp3902) 		 
Short Communications

$L^p$-Valued Random Measures and Good Extensions of a Stochastic Basis

V. A. Lebedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (890 kB)
DOI: https://doi.org/10.4213/tvp3902
Abstract: In this paper, a development of the author's paper [Theory Probab. Appl., 40 (1995), pp. 645–652], we prove the existence of an extension of an $L^p$-valued random measure $\theta$ in the sense of Bichteler and Jacod [Theory and Application of Random Fields, Lecture Notes in Control and Inform. Sci. 49, Springer, Berlin, 1983, pp. 1–18] under a good (with respect to $\theta$) extension of a stochastic basis. Our main result, Theorem 2, was announced in [V. A. Lebedev, Proc. 22nd European Meeting of Statisticians and 7th Vilnius Conference on Probability Theory and Mathematical Statistics: Abstracts of Communications, TEV, Vilnius, 1998, p. 298].
Keywords: good stopping time, $\sigma$-finite $L^p$-valued random measure, good extension of a stochastic basis, extension of a random measure.
Received: 16.06.1997
Revised: 17.11.2000
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 3, Pages 536–542
DOI: https://doi.org/10.1137/S0040585X97979147
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Lebedev, “$L^p$-Valued Random Measures and Good Extensions of a Stochastic Basis”, Teor. Veroyatnost. i Primenen., 46:3 (2001), 563–568; Theory Probab. Appl., 46:3 (2002), 536–542
Citation in format AMSBIB
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