Weak uniqueness of martingale solutions to stochastic partial differential equations in Hilbert spaces
Teoriâ slučajnyh processov, Tome 25 (2020) no. 1, pp. 78-89.

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We prove the uniqueness of martingale solutions for stochastic partial differential equations generalizing the work in Mandrekar and Skorokhod (1998). The main idea used is to reduce this problem to the case in Mandrekar and Skorokhod using the techniques introduced in Filipović et al. (2010).
Keywords: Stochastic partial differential equation, Stochastic differential equation, weak uniqueness.
Mots-clés : martingale solution
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V. Mandrekar; U. V. Naik-Nimbalkar. Weak uniqueness of martingale solutions to stochastic partial differential equations in Hilbert spaces. Teoriâ slučajnyh processov, Tome 25 (2020) no. 1, pp. 78-89. http://geodesic.mathdoc.fr/item/THSP_2020_25_1_a3/

[1] D. Filipović, S. Tappe, J. Teichmann, “Jump-diffusions in Hilbert spaces: existence, stability and numerics”, Stochastics, 82:5 (2010), 475–520 | DOI | MR

[2] L. Gawarecki, V. Mandrekar, Stochastic differential equations in infinite dimensions, Springer, Springer-Verlag, Berlin, Heidelberg, 2011 | MR

[3] Springer-Verlag, New York Inc, 1979 | MR

[4] V. Mandrekar, A. V. Skorokhod, “An approach to the martingale problem for diffusion stochastic equations in a Hilbert space”, Theory of Stochastic Processes, 4:20 (1998), 54–59 | MR

[5] D. W. Stroock, S. R. S. Varadhan, “Diffusion processes with continuous coefficients I”, Pure. and Appl. Math., 12 (1969), 345–400 | DOI | MR

[6] B. Sz.-Nagy, C. Foias, Harmonic analysis of operators on Hilbert space, Second Edition, Springer, New York, 2010 | MR

[7] S. Tappe, “The Yamada-Watanabe Theorem for mild solutions to stochastic partial differential equations”, Electronic Communications in Probability, 18:24 (2013), 1–13 | MR