Abstract
We prove a Yamada-Watanabe theorem for forward-backward stochastic differential equations (FBSDEs). As a consequence, we show that weak existence and pathwise uniqueness of the solution imply the existence of a strong solution. We use this result to establish existence and uniqueness of weak solutions for a large class of FBSDEs. We also give a probabilistic interpretation of the solutions of certain nonlinear partial differential equations (PDEs).
| Original language | English |
|---|---|
| Pages (from-to) | 271-285 |
| Number of pages | 15 |
| Journal | Random Operators and Stochastic Equations |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| State | Published - Oct 2007 |
| Externally published | Yes |
Bibliographical note
Funding Information:Second author: Supported by MENA Swedish-Algerian Partnership Program (348-2002-6874).
Keywords
- Burgers equation
- Forward-backward stochastic differential equation
- Girsanov theorem
- Weak solution
- Yamada-Watanabe theorem
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
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