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 show that the Gibbs measure of the stochastic hyperbolicsine-Gordon equation on the circle is the unique invariant measure for theMarkov process. Moreover, the Markov transition probabilities convergeexponentially fast to the unique invariant measure in a type of 1-Wassersteindistance. The main difficulty comes from the fact that the hyperbolic dynamicsdoes not satisfy the strong Feller property even if sufficiently manydirections in a phase space are forced by the space-time white noise forcing.We instead establish that solutions give rise to a Markov process whosetransition semigroup satisfies the asymptotic strong Feller property andconvergence to equilibrium in a type of Wasserstein distance.

Exponential ergodicity for the stochastic hyperbolic sine-Gordon equation on the circle