Nonlinear stochastic wave equation driven by rough noise

Liu, Shuhui; Hu, Yaozhong; Wang, Xiong

doi:10.1016/j.jde.2022.05.016

Cited by 3 publications

(1 citation statement)

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“…When H 0 = 1 2 (i.e., the noise is white in time) and d = 1, the necessary and sufficient condition for the existence of solutions to PAM and HAM is known as H 1 > 1 4 . The readers are referred to [5,6,22,23,30,32] for further results. On the other hand when H 0 = 1/2 and d > 1, it is known ( [15]) that the number of Hurst parameters that are less than 1/2 can be at most 1 for (1.1) to be solvable.…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions to solve parabolic Anderson model with rough noise

Liu¹,

Hu²,

Wang³

2022

Preprint

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We obtain necessary and sufficient conditions for the existence of n-th chaos of the solution to the parabolic Anderson model, where Ẇ (t, x) is a fractional Brownian field with temporal Hurst parameter H 0 ≥ 1/2 and spatial parameters, we extend the condition on the parameters under which the chaos expansion of the solution is convergent in the mean square sense, which is both sufficient and necessary under some circumstances.

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Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions to solve parabolic Anderson model with rough noise

Liu¹,

Hu²,

Wang³

2022

Preprint

Self Cite

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A Large Deviation Principle for the Stochastic Heat Equation with General Rough Noise

Wang

Zhang

2023

J Theor Probab

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We study Freidlin-Wentzell's large deviation principle for one dimensional nonlinear stochastic heat equation driven by a Gaussian noise:where 9 W is white in time and fractional in space with Hurst parameter H P p 1 4 , 1 2 q. Recently, Hu and Wang (Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022) 379-423) studied the wellposedness of this equation without the technical condition of σp0q " 0 which was previously assumed in Hu et al. (Ann. Probab. 45 (2017) 4561-4616). We adopt a new sufficient condition proposed by Matoussi et al. (Appl. Math. Optim. 83 (2021) 849-879) for the weak convergence criterion of the large deviation principle.

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