English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we consider the following stochastic partial differentialequation (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 theabove 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 onWong-Zakai theorem and the support theorem for diffusion processes with N.V.Krylov's $L_p$-theory of SPDEs.

Wong-Zakai approximation and support theorem for semilinear SPDEs with finite dimensional noise in the whole space