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- W2888751664 abstract "In this paper we consider the following stochastic partial differential equation (SPDE) in the whole space: $du (t, x) = [a^{i j} (t, x) D_{i j} u(t, x) + f(u, t, x)], dt + sum_{k = 1}^m g^k (u(t, x)) dw^k (t).$ We prove the convergence of a Wong-Zakai type approximation scheme of the above equation in the space $ C^{theta } ([0, T], H^{gamma}_p (mathbb{R}^d)) $ in probability, for some $ theta in (0,1/2), gamma in (1, 2)$, and $p > 2$. We also prove a Stroock-Varadhan's type support theorem. To prove the results we combine V. Mackevicius ideas from his papers on Wong-Zakai theorem and the support theorem for diffusion processes with N.V. Krylov's $L_p$-theory of SPDEs." @default.
- W2888751664 created "2018-08-31" @default.
- W2888751664 creator A5053868921 @default.
- W2888751664 date "2018-08-22" @default.
- W2888751664 modified "2023-10-15" @default.
- W2888751664 title "Wong-Zakai approximation and support theorem for semilinear SPDEs with finite dimensional noise in the whole space" @default.
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