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/

Zendy Plus

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

Zendy Tools

Zendy Open

We analyze the long-time behavior of numerical schemes for a class ofmonotone stochastic partial differential equations (SPDEs) driven bymultiplicative noise. By deriving several time-independent a priori estimatesfor the numerical solutions, combined with the ergodic theory of Markovprocesses, we establish the exponential ergodicity of these schemes with aunique invariant measure, respectively. Applying these results to thestochastic Allen--Cahn equation indicates that these schemes always have atleast one invariant measure, respectively, and converge strongly to the exactsolution with sharp time-independent rates. We also show that these numericalinvariant measures are exponentially ergodic and thus give an affirmativeanswer to a question proposed in (J. Cui, J. Hong, and L. Sun, StochasticProcess. Appl. (2021): 55--93), provided that the interface thickness is nottoo small.

Numerical Ergodicity and Uniform Estimate of Monotone SPDEs Driven by Multiplicative Noise