Weak and strong solutions of stochastic differential equations: Existence and stability

1981 ◽  
pp. 169-212 ◽  
Author(s):  
Jean Jacod ◽  
Jean Memin
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solutions ◽  
Existence And Stability ◽  
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.

scholarly journals Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Elhoussain Arhrrabi ◽  
M’hamed Elomari ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Stability Of Solutions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Existence And Stability ◽  
Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

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