Extremal behavior of the heat random field
type: Item
instance of: scholarly article
title: Extremal behavior of the heat random field
zbMATH Open document ID: 1115.60054
author: Yu. V. Kozachenko
author: G. M. Leonenko
published in: Extremes
publication date: 2007-05-29T00:00:00Z
review text: The authors consider the Cauchy problem for the \(n\)-dimensional heat equation \({\partial u\over\partial t}=\mu\Delta u\), \(t>0\), \(x\in \mathbb R^{n}\), \(\mu>0\), subject to the random initial condition \(u(0,x)=\eta(x)\), \(x\in \mathbb R^{n}\), where \(u=u(t,x)\), \(t>0\), \(x\in \mathbb R^{n}\); \(\Delta\) is Laplacian and \(\eta(x)\), \(x\in \mathbb R^{n}\), is a random field. The exponential type inequality for the distribution of the supremum of the solution of the considered Cauchy problem is obtained.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 5158676
zbMATH Keywords: heat equation
zbMATH Keywords: random initial condition
zbMATH Keywords: sub-Gaussian random field
zbMATH Keywords: distribution of supremum
zbMATH Keywords: exponential inequality
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s10687-006-7967-8
OpenAlex ID: W2043870561
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DOI: 10.1007/S10687-006-7967-8
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description: scientific article; zbMATH DE number 5158676