Spatial asymptotic of the stochastic heat equation with compactly supported initial data

Jingyu Huang; Khoa Lê

doi:10.1007/s40072-019-00133-x

Spatial asymptotic of the stochastic heat equation with compactly supported initial data

Jingyu Huang, Khoa Lê

Mathematics

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Abstract

We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white in time and correlated in space. The spatial correlation function is either bounded or non-negative satisfying Dalang’s condition. The initial data are Borel measures with compact supports, in particular, include Dirac masses. The results obtained are related to those of Conus et al. (Ann Probab 41(3B):2225–2260, 2013) and Chen (Ann Probab 44(2):1535–1598, 2016) where constant initial data are considered.

Original language	English
Pages (from-to)	495-539
Number of pages	45
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	7
Issue number	3
Early online date	2 Mar 2019
DOIs	https://doi.org/10.1007/s40072-019-00133-x
Publication status	Published - 15 Sept 2019

Keywords

Parabolic Anderson model
Feynman–Kac representation ·
Brownian motion
Spatial asymptotic

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title = "Spatial asymptotic of the stochastic heat equation with compactly supported initial data",

abstract = "We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white in time and correlated in space. The spatial correlation function is either bounded or non-negative satisfying Dalang{\textquoteright}s condition. The initial data are Borel measures with compact supports, in particular, include Dirac masses. The results obtained are related to those of Conus et al. (Ann Probab 41(3B):2225–2260, 2013) and Chen (Ann Probab 44(2):1535–1598, 2016) where constant initial data are considered.",

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AU - Huang, Jingyu

AU - Lê, Khoa

PY - 2019/9/15

Y1 - 2019/9/15

N2 - We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white in time and correlated in space. The spatial correlation function is either bounded or non-negative satisfying Dalang’s condition. The initial data are Borel measures with compact supports, in particular, include Dirac masses. The results obtained are related to those of Conus et al. (Ann Probab 41(3B):2225–2260, 2013) and Chen (Ann Probab 44(2):1535–1598, 2016) where constant initial data are considered.

AB - We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white in time and correlated in space. The spatial correlation function is either bounded or non-negative satisfying Dalang’s condition. The initial data are Borel measures with compact supports, in particular, include Dirac masses. The results obtained are related to those of Conus et al. (Ann Probab 41(3B):2225–2260, 2013) and Chen (Ann Probab 44(2):1535–1598, 2016) where constant initial data are considered.

KW - Parabolic Anderson model

KW - Feynman–Kac representation ·

KW - Brownian motion

KW - Spatial asymptotic

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DO - 10.1007/s40072-019-00133-x

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JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 3

ER -

Spatial asymptotic of the stochastic heat equation with compactly supported initial data

Abstract

Keywords

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