A stochastic heat equation with the distributions of Lévy processes as its invariant measures

Tadahisa Funaki; Bin Xie

doi:10.1016/j.spa.2008.02.007

A stochastic heat equation with the distributions of Lévy processes as its invariant measures

Tadahisa Funaki^*, Bin Xie

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of Lévy processes. Our assumption on the corresponding Lévy measure is, in general, mild except that we need its integrability to show that the distributions of Lévy processes are the only invariant measures of the stochastic heat equation.

Original language	English
Pages (from-to)	307-326
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	119
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2008.02.007
Publication status	Published - 2009 Feb
Externally published	Yes

Keywords

Lévy process
Stochastic heat equation
Stochastic partial differential equation

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2008.02.007

Cite this

@article{5efd1019f1374a3884385aabac47d3d6,

title = "A stochastic heat equation with the distributions of L{\'e}vy processes as its invariant measures",

abstract = "We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of L{\'e}vy processes. Our assumption on the corresponding L{\'e}vy measure is, in general, mild except that we need its integrability to show that the distributions of L{\'e}vy processes are the only invariant measures of the stochastic heat equation.",

keywords = "L{\'e}vy process, Stochastic heat equation, Stochastic partial differential equation",

author = "Tadahisa Funaki and Bin Xie",

year = "2009",

month = feb,

doi = "10.1016/j.spa.2008.02.007",

language = "English",

volume = "119",

pages = "307--326",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - A stochastic heat equation with the distributions of Lévy processes as its invariant measures

AU - Funaki, Tadahisa

AU - Xie, Bin

PY - 2009/2

Y1 - 2009/2

N2 - We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of Lévy processes. Our assumption on the corresponding Lévy measure is, in general, mild except that we need its integrability to show that the distributions of Lévy processes are the only invariant measures of the stochastic heat equation.

AB - We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of Lévy processes. Our assumption on the corresponding Lévy measure is, in general, mild except that we need its integrability to show that the distributions of Lévy processes are the only invariant measures of the stochastic heat equation.

KW - Lévy process

KW - Stochastic heat equation

KW - Stochastic partial differential equation

UR - http://www.scopus.com/inward/record.url?scp=58549093371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58549093371&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2008.02.007

DO - 10.1016/j.spa.2008.02.007

M3 - Article

AN - SCOPUS:58549093371

SN - 0304-4149

VL - 119

SP - 307

EP - 326

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

A stochastic heat equation with the distributions of Lévy processes as its invariant measures

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this