26. balan.chen.ea:22:parabolic#
Parabolic Anderson model with rough noise in space and rough initial conditions
Raluca Balan, Le Chen, Yiping Ma
Abstract: In this note, we consider the parabolic Anderson model on \(\mathbb{R}_{+} \times \mathbb{R}\), driven by a Gaussian noise which is fractional in time with index \(H_0>1/2\) and fractional in space with index \(0<H<1/2\) such that \(H_0+H>3/4\). Under a general condition on the initial data, we prove the existence and uniqueness of the mild solution and obtain its exponential upper bounds in time for all \(p\)-th moments with \(p\ge 2\).
MSC 2010 subject classifications: Primary. 60H15; Secondary. 60H07.
Keywords: stochastic partial differential equations, parabolic Anderson model, Malliavin calculus, rough initial condition, Dirac delta initial condition, rough Gaussian noise.
[BCM22] Balan, Raluca, Chen, Le & Ma, Yiping (2022) ‘Parabolic Anderson model with rough noise in space and rough initial conditions’, Electron. Commun. Probab. 27, Paper No. 65, 12. <https://doi.org/10.1214/22-ecp506>
@article{balan.chen.ea:22:parabolic,
author = {Balan, Raluca and Chen, Le and Ma, Yiping},
title = {Parabolic {A}nderson model with rough noise in space and rough initial conditions},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {27},
year = {2022},
pages = {Paper No. 65, 12},
mrclass = {60H15 (60H07)},
mrnumber = {4529633},
doi = {10.1214/22-ecp506},
url = {https://doi.org/10.1214/22-ecp506}
}
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