5. chen.khoshnevisan.ea:16:decorrelation#
Decorrelation of total mass via energy
Le Chen, Davar Khoshnevisan, and Kunwoo Kim
Abstract: The main result of this small note is a quantified version of the assertion that if \(u\) and \(v\) solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of the two systems are nearly uncorrelated for a very long time. One of the consequences of this fact is that a stochastic heat equation with regular coefficients is a finite system if and only if the initial state is integrable.
MSC 2010 subject classifications: Primary 60H15, 60H25; Secondary 35R60, 60K37, 60J30, 60B15.
Keywords: stochastic heat equation, finite particle systems, total mass, mutual energy.
[CKK16] Chen, Le, Khoshnevisan, Davar & Kim, Kunwoo (2016) ‘Decorrelation of total mass via energy’, Potential Anal. 45, 157–166. <https://doi.org/10.1007/s11118-016-9540-7>
@article{chen.khoshnevisan.ea:16:decorrelation,
author = {Chen, Le and Khoshnevisan, Davar and Kim, Kunwoo},
title = {Decorrelation of total mass via energy},
journal = {Potential Anal.},
fjournal = {Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis},
volume = {45},
year = {2016},
number = {1},
pages = {157--166},
issn = {0926-2601},
mrclass = {60H15 (35K10 35R60 60B15 60H25 60K37)},
mrnumber = {3511809},
mrreviewer = {Ya. \={I}. B\={i}lopol{\cprime}s{\cprime}ka},
doi = {10.1007/s11118-016-9540-7},
url = {https://doi.org/10.1007/s11118-016-9540-7}
}
References: Chen and Dalang [CD15b]; Chen and Kim [CK17]; Dalang [Dal99]; Dalang and Mueller [DM03]; Donoho and Stark [DS89]; Foondun and Khoshnevisan [FK09]; Fukushima et al. [FOT94]; Khoshnevisan [Kho09]; Liggett [Lig05]; Mueller [Mue91b]; Mueller [Mue09]; Spitzer [Spi81]; Walsh [Wal86];