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On existence of solutions of multivalued stochastic differential equations with discontinuous coefficients

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The subject of the paper is to find existence conditions of weak solutions to multivalued stochastic differential equations with discontinuous coefficients. First we prove that a non-exploding solution exists when the drift coefficient b satisfies linear growth and the diffusion coefficient σ is uniformly elliptic. On this basis, we continue to obtain a solution (up to the explosion time) in the weak sense under certain local integrability, improving the result of Rozkosz and Słomiński.
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Keywords: Krylov's estimate; Skorohod's theorem; multivalued stochastic differential equation; primary 60H10; secondary 47H04; tightness; weak convergence; weak solution

Document Type: Research Article

Affiliations: School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, Guangdong,510275, P.R. China

Publication date: March 4, 2014

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