Kavli Affiliate: Ran Wang
| First 5 Authors: Ruinan Li, Ran Wang, Beibei Zhang, ,
| Summary:
We study Freidlin-Wentzell’s large deviation principle for one dimensional
nonlinear stochastic heat equation driven by a Gaussian noise: $$frac{partial
u^varepsilon(t,x)}{partial t} = frac{partial^2 u^varepsilon(t,x)}{partial
x^2}+sqrt{varepsilon} sigma(t, x, u^varepsilon(t,x))dot{W}(t,x),quad t>
0,, xinmathbb{R},$$ where $dot W$ is white in time and fractional in space
with Hurst parameter $Hin(frac 14,frac 12)$. Recently, Hu and Wang ({it
Ann. Inst. Henri Poincar’e Probab. Stat.} {bf 58} (2022) 379-423) studied the
well-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 by
Matoussi et al. ({it Appl. Math. Optim.} textbf{83} (2021) 849-879) for the
weak convergence criterion of the large deviation principle.
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