On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations
| Autor: | Moritz Ritter, David Criens |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Pure mathematics General Mathematics 010102 general mathematics Probability (math.PR) Banach space 01 natural sciences Dual (category theory) Stochastic partial differential equation 010104 statistics & probability FOS: Mathematics Uniqueness 0101 mathematics Statistics Probability and Uncertainty Martingale (probability theory) Brownian motion Mathematics - Probability Mathematics |
| Popis: | We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The solutions are allowed to take values in Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny’s and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada–Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|