8. chen.khoshnevisan.ea:17:boundedness#
A boundedness trichotomy for the stochastic heat equation
Le Chen, Davar Khoshnevisan, and Kunwoo Kim
Abstract: We consider the stochastic heat equation with a multiplicative white noise forcing term under standard ‘’intermitency conditions’’. The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution \(x\mapsto u(t\,,x)\) can be characterized generically by the decay rate, at \(\pm\infty\), of the initial function \(u_0\). More specifically, we prove that there are three generic boundedness regimes, depending on the numerical value of
MSC 2010 subject classifications: Primary 60H15. Secondary 35R60.
Keywords: stochastic heat equation.
[CKK17] Chen, Le, Khoshnevisan, Davar & Kim, Kunwoo (2017) ‘A boundedness trichotomy for the stochastic heat equation’, Ann. Inst. Henri Poincar’e Probab. Stat. 53, 1991–2004. <https://doi.org/10.1214/16-AIHP780>
@article{chen.khoshnevisan.ea:17:boundedness,
author = {Chen, Le and Khoshnevisan, Davar and Kim, Kunwoo},
title = {A boundedness trichotomy for the stochastic heat equation},
journal = {Ann. Inst. Henri Poincar\'{e} Probab. Stat.},
fjournal = {Annales de l'Institut Henri Poincar\'{e} Probabilit\'{e}s et Statistiques},
volume = {53},
year = {2017},
number = {4},
pages = {1991--2004},
issn = {0246-0203},
mrclass = {60H15 (35R60)},
mrnumber = {3729644},
mrreviewer = {Paul Andr\'{e} Razafimandimby},
doi = {10.1214/16-AIHP780},
url = {https://doi.org/10.1214/16-AIHP780}
}
References: Chen and Dalang [CD14a]; Chen and Dalang [CD15b]; Conus and Khoshnevisan [CK12]; Dareiotis and Gerencsér [DG15]; Foondun and Khoshnevisan [FK09]; Foondun and Khoshnevisan [FK10]; Joseph et al. [JKM17]; Khoshnevisan [Kho14]; Mueller [Mue91b]; Mueller [Mue09]; Shiga [Shi92]; Walsh [Wal86];