  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.
