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

In this article, we study the stochastic wave equation in arbitrary spatialdimension $d$, with a multiplicative term of the form $\sigma(u)=u$, also knownin the literature as the Hyperbolic Anderson Model. This equation is perturbedby a general Gaussian noise, which is homogeneous in both space and time. Weprove the existence and uniqueness of a solution of this equation (in theSkorohod sense) and the H\"older continuity of its sample paths, under the samerespective conditions on the spatial spectral measure of the noise as in thecase of the white noise in time, regardless of the temporal covariance functionof the noise.

Hyperbolic Anderson Model with space-time homogeneous Gaussian noise