TY  - JOUR
AB  - We prove that joint uniqueness in law and the existence of a strong solution imply pathwise uniqueness for variational solutions to stochastic partial differential equations of type dXt = b(t, X)dt + s(t, X)dWt, t = 0, and show that for such equations uniqueness in law is equivalent to joint uniqueness in law for deterministic initial conditions. Here W is a cylindrical Wiener process in a separable Hilbert space U and the equation is considered in a Gelfand triple V. H. E, where H is some separable (infinite-dimensional) Hilbert space. This generalizes the corresponding results of Cherny, who proved these statements for the case of finite-dimensional equations.
DA  - 2021
DO  - 10.1007/s40072-020-00167-6
KW  - Stochastic partial differential equations
KW  - Yamada-Watanabe theorem
KW  - Pathwise uniqueness
KW  - Uniqueness in law
KW  - Joint uniqueness in law
KW  - Variational solutions
LA  - eng
M2  - 33
PY  - 2021
SN  - 2194-0401
SP  - 33-70
T2  - Stochastics and Partial Differential Equations: Analysis and Computations
TI  - On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29418830
Y2  - 2024-11-21T22:49:27
ER  -