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
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U2 - 10.1016/j.spa.2008.02.007
DO - 10.1016/j.spa.2008.02.007
M3 - Article
AN - SCOPUS:58549093371
VL - 119
SP - 307
EP - 326
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 2
ER -