Matyas Barczy, Zenghu Li, Gyula Pap
Published 2013-12-16, updated 2014-11-29Version 3
Recently, Kurtz (2007, 2014) obtained a general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations covering also the case of stochastic differential equations with jumps. Following the original method of Yamada and Watanabe (1971), we give alternative proofs for the following two statements: pathwise uniqueness implies uniqueness in the sense of probability law, and weak existence together with pathwise uniqueness imply strong existence for stochastic differential equations with jumps.
$\varphi$-strong solutions and uniqueness of 1-dimensional stochastic differential equations
Stochastic differential equations with coefficients in Sobolev spaces
Strong solutions for stochastic differential equations with jumps
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