On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe

Rehmeier M (2021)
Stochastics and Partial Differential Equations: Analysis and Computations 9: 33-70.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
Stochastic partial differential equations; Yamada-Watanabe theorem; Pathwise uniqueness; Uniqueness in law; Joint uniqueness in law; Variational solutions
Erscheinungsjahr
2021
Zeitschriftentitel
Stochastics and Partial Differential Equations: Analysis and Computations
Band
9
Seite(n)
33-70
ISSN
2194-0401
eISSN
2194-041X
Page URI
https://pub.uni-bielefeld.de/record/2941883

Zitieren

Rehmeier M. On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations . 2021;9:33-70.
Rehmeier, M. (2021). On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations , 9, 33-70. https://doi.org/10.1007/s40072-020-00167-6
Rehmeier, M. (2021). On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations 9, 33-70.
Rehmeier, M., 2021. On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations , 9, p 33-70.
M. Rehmeier, “On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe”, Stochastics and Partial Differential Equations: Analysis and Computations , vol. 9, 2021, pp. 33-70.
Rehmeier, M.: On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations . 9, 33-70 (2021).
Rehmeier, Marco. “On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe”. Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021): 33-70.
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2021-03-18T10:35:05Z
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