35. chen.xia:23:asymptotic#
Asymptotic properties of stochastic partial differential equations in the sublinear regime
Le Chen and Panqiu Xia
To appear in Annals of Probability
Abstract: In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic properties for the solutions. These results shed light on the smoothing intermittency effect under weak diffusion (i.e., sublinear growth) previously observed by Zeldovich et al. [ZMRS87]. The sample-path spatial asymptotics obtained in this paper partially bridge a gap in earlier works of Conus et al. [CJK13, CJKS13b], which focused on two extreme scenarios: a linear diffusion coefficient and a bounded diffusion coefficient. Our approach is highly robust and applicable to a variety of stochastic partial differential equations, including the one-dimensional stochastic wave equation and the stochastic fractional diffusion equations.
MSC 2010 subject classifications: Primary 60H15; Secondary 35R60.
Keywords: stochastic partial differential equations, sublinear growth, asymptotic concavity, moment bounds, intermittency, spatial asymptotics.
[CX23] Le Chen & Panqiu Xia (2023) ‘Asymptotic properties of stochastic partial differential equations in the sublinear regime’, preprint arXiv:2306.06761
@article{chen.xia:23:asymptotic,
title = {Asymptotic properties of stochastic partial differential equations in the sublinear regime},
author = {Le Chen and Panqiu Xia},
year = {2023},
month = {June},
journal = {preprint arXiv:2306.06761},
url = {http://arXiv.org/abs/2306.06761}
}
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