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

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

DOI: 10.4213/tvp3774

 English version: Theory of Probability and its Applications, 2003, 47:4, 637–648

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