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

In this paper, we establish lower and upper Gaussian bounds for theprobability density of the mild solution to the stochastic heat equation withmultiplicative noise and in any space dimension. The driving perturbation is aGaussian noise which is white in time with some spatially homogeneouscovariance. These estimates are obtained using tools of the Malliavin calculus.The most challenging part is the lower bound, which is obtained by adapting ageneral method developed by Kohatsu-Higa to the underlying spatiallyhomogeneous Gaussian setting. Both lower and upper estimates have the sameform: a Gaussian density with a variance which is equal to that of the mildsolution of the corresponding linear equation with additive noise.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension