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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 4, Pages 672–685
DOI: https://doi.org/10.4213/tvp3774 (Mi tvp3774) 		 
On the existence of weak solutions for stochastic differential equations with driving $L^0$-valued measures

V. A. Lebedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (1481 kB)
DOI: https://doi.org/10.4213/tvp3774
Abstract: In this paper, for a stochastic differential equation with a $\sigma$-finite $L^0$-valued random measure $\theta$ in the sense of Bichteler and Jacod, a proof of the existence of its weak solution is given, which is based on a similar result for the particular case of an $L^2$-valued random measure.
Keywords: $\sigma$-finite $L^p$-valued random measure, stochastic differential equation, weak solution, extension of a stochastic basis.
Received: 26.03.1999
Revised: 23.05.2000
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 4, Pages 637–648
DOI: https://doi.org/10.1137/S0040585X97980002
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Lebedev, “On the existence of weak solutions for stochastic differential equations with driving $L^0$-valued measures”, Teor. Veroyatnost. i Primenen., 47:4 (2002), 672–685; Theory Probab. Appl., 47:4 (2003), 637–648
Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2003
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\issue 4
\pages 637--648
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  • https://www.mathnet.ru/eng/tvp/v47/i4/p672
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