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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Strong convergence rates for numerical approximations of semilinearstochastic partial differential equations (SPDEs) with smooth and regularnonlinearities are well understood in the literature. Weak convergence ratesfor numerical approximations of such SPDEs have been investigated for about twodecades and are still not yet fully understood. In particular, no essentiallysharp weak convergence rates are known for temporal or spatial numericalapproximations of space-time white noise driven SPDEs with nonlinearmultiplication operators in the diffusion coefficients. In this article weovercome this problem by establishing essentially sharp weak convergence ratesfor exponential Euler approximations of semilinear SPDEs with nonlinearmultiplication operators in the diffusion coefficients. Key ingredients of ourapproach are applications of the mild It\^{o} type formula in UMD Banach spaceswith type 2.

Weak convergence rates for numerical approximations of stochastic  partial differential equations with nonlinear diffusion coefficients in UMD  Banach spaces