NDLI: -measures for branching exit Markov systems and their applications to differential equations

Content Provider	Springer Nature Link
Author	Dynkin, E.B. Kuznetsov, S.E.
Copyright Year	2004
Abstract	Semilinear equations Lu=ψ(u) where L is an elliptic differential operator and ψ is a positive function can be investigated by using (L,ψ)-superdiffusions. In a special case Δu=u2 a powerful probabilistic tool – the Brownian snake – introduced by Le Gall was successfully applied by him and his school to get deep results on solutions of this equation. Some of these results (but not all of them) were extended by Dynkin and Kuznetsov to general equations by applying superprocesses. An important role in the theory of the Brownian snake and its applications is played by measures x on the space of continuous paths. Our goal is to introduce analogous measures related to superprocesses (and to general branching exit Markov systems). They are defined on the space of measures and we call them -measures. Using -measures allows to combine some advantages of Brownian snakes and of superprocesses as tools for a study of semilinear PDEs.
Starting Page	135
Ending Page	150
Page Count	16
File Format	PDF
ISSN	01788051
Journal	Probability Theory and Related Fields
Volume Number	130
Issue Number	1
e-ISSN	14322064
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-03-03
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Semilinear Elliptic PDEs Infinitely divisible Random Measures -measures
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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