MARKOV SNAKES AND SUPERPROCESSES

Citation
Eb. Dynkin et Se. Kuznetsov, MARKOV SNAKES AND SUPERPROCESSES, Probability theory and related fields, 103(4), 1995, pp. 433-473
Citations number
35
Categorie Soggetti
Statistic & Probability","Statistic & Probability
ISSN journal
01788051
Volume
103
Issue
4
Year of publication
1995
Pages
433 - 473
Database
ISI
SICI code
0178-8051(1995)103:4<433:MSAS>2.0.ZU;2-C
Abstract
We suggest the name Markov snakes for a class of path-valued Markov pr ocesses introduced recently by J.-F. Le Gall in connection with the th eory of branching measure-valued processes. Le Gall applied this class to investigate path properties of superdiffusions and to approach pro babilistically partial differential equations involving a nonlinear op erator Delta v - v(2). We establish an isomorphism theorem which allow s to translate results on continuous superprocesses into the language of Markov snakes and vice versa. By using this theorem, we get limit t heorems for discrete Markov snakes.