Weak and strong solutions of stochastic differential equations

Stochastics ◽  
1980 ◽  
Vol 3 (1-4) ◽  
pp. 171-191 ◽  
Author(s):  
Jacod Jean
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solutions ◽  
Weak And Strong Solutions

scholarly journals Yamada-Watanabe Results for Stochastic Differential Equations with Jumps

2015 ◽  
Vol 2015 ◽  
pp. 1-23 ◽  
Author(s):  
Mátyás Barczy ◽  
Zenghu Li ◽  
Gyula Pap
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Stochastic Equations ◽  
Original Method ◽  
Pathwise Uniqueness ◽  
General Version ◽  
Strong Existence ◽  
Weak And Strong Solutions

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 implies strong existence for stochastic differential equations with jumps.

Sign in / Sign up

Export Citation Format

Share Document