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

We study Freidlin-Wentzell's large deviation principle for one dimensionalnonlinear stochastic heat equation driven by a Gaussian noise: $$\frac{\partialu^\varepsilon(t,x)}{\partial t} = \frac{\partial^2 u^\varepsilon(t,x)}{\partialx^2}+\sqrt{\varepsilon} \sigma(t, x, u^\varepsilon(t,x))\dot{W}(t,x),\quad t>0,\, x\in\mathbb{R},$$ where $\dot W$ is white in time and fractional in spacewith Hurst parameter $H\in(\frac 14,\frac 12)$. Recently, Hu and Wang ({\itAnn. Inst. Henri Poincar\'e Probab. Stat.} {\bf 58} (2022) 379-423) studied thewell-posedness of this equation without the technical condition of$\sigma(0)=0$ which was previously assumed in Hu et al. ({\it Ann. Probab}.{\bf 45} (2017) 4561-4616). We adopt a new sufficient condition proposed byMatoussi et al. ({\it Appl. Math. Optim.} \textbf{83} (2021) 849-879) for theweak convergence criterion of the large deviation principle.

A large deviation principle for the stochastic heat equation with general rough noise