Geodesic
On the existence of weak solutions for stochastic differential equations with driving $L^0$-valued measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 672-685

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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. 
@article{TVP_2002_47_4_a2,
     author = {V. A. Lebedev},
     title = {On the existence of weak solutions for stochastic differential equations with driving $L^0$-valued measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {672--685},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a2/}
}
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V. A. Lebedev. On the existence of weak solutions for stochastic differential equations with driving $L^0$-valued measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 672-685. http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a2/