This article is cited in 6 papers

Behavior of random measures under filtration change

V. A. Lebedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, we study the problem of the behavior of $L^p $-valued random measures in the sense of Bichteler and Jacod [Lecture Notes in Control Inform. Sci., 49 (1983), pp. 1–18] and stochastic integrals with respect to them under filtration change and thus give a complete proof of the main result announced by the author in [First World Congress of the Bernoulli Society of Mathematical Statistics and Probability Theory (Abstracts), Vol. II, Nauka, Moscow, 1986, p. 734].

Keywords: $\sigma$-finite $L^p$-valued random measure, its decomposition, its extension for enlargement of a filtration.

Received: 11.01.1993

 English version: Theory of Probability and its Applications, 1995, 40:4, 645–652

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