$L^p$-Valued Random Measures and Good Extensions of a Stochastic Basis
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 563-568
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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.
@article{TVP_2001_46_3_a9,
author = {V. A. Lebedev},
title = {$L^p${-Valued} {Random} {Measures} and {Good} {Extensions} of a {Stochastic} {Basis}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {563--568},
publisher = {mathdoc},
volume = {46},
number = {3},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a9/}
}
V. A. Lebedev. $L^p$-Valued Random Measures and Good Extensions of a Stochastic Basis. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 563-568. http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a9/