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

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

DOI: 10.4213/tvp3902

 English version: Theory of Probability and its Applications, 2002, 46:3, 536–542

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