Stochastic partial differential equations for superprocesses in random environments

We study a superprocess, X t (dx) on R 1 generated by a particle picture whose branching mechanisms are affected by certain random environments. We show that under suitable conditions X t (dx) is absolutely continuous with respect to Lebesgue measure and has a continuous density function for each t...

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Bibliographic Details
Published inStochastic analysis and applications Vol. 20; no. 1; pp. 145 - 163
Main Authors Kwon, Youngmee, Cho, Nhansook, Kang, Hye-Jeong
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 21.03.2002
Taylor & Francis
Subjects
AMS Subject Classifications: Primary 60J60
Exact sciences and technology
Martingale problem
Mathematics
Measure-valued process
Sciences and techniques of general use
Secondary 60G55
Stochastic partial differential equation
Superprocesses
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ISSN0736-2994
1532-9356
DOI10.1081/SAP-120002425

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Summary:We study a superprocess, X t (dx) on R 1 generated by a particle picture whose branching mechanisms are affected by certain random environments. We show that under suitable conditions X t (dx) is absolutely continuous with respect to Lebesgue measure and has a continuous density function for each t almost surely. In addition we derive a stochastic partial differential equation whose solution is X t and a limit problem.
ISSN:0736-2994
1532-9356
DOI:10.1081/SAP-120002425