Feller property and infinitesimal generator of the exploration process

Romain Abraham; Jean François Delmas

doi:10.1007/s10959-007-0082-1

Feller property and infinitesimal generator of the exploration process

Romain Abraham, Jean François Delmas

conventionnée avec l'Université d'Orléans

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

Abstract

We consider the exploration process associated to the continuous random tree (CRT) built using a Lévy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale.

Original language	English
Pages (from-to)	355-370
Number of pages	16
Journal	Journal of Theoretical Probability
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s10959-007-0082-1
Publication status	Published - 1 Jun 2007

Keywords

Exploration process
Feller property
Infinitesimal generator
Lévy snake
Measure valued process

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10.1007/s10959-007-0082-1

Cite this

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abstract = "We consider the exploration process associated to the continuous random tree (CRT) built using a L{\'e}vy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale.",

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AB - We consider the exploration process associated to the continuous random tree (CRT) built using a Lévy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale.

KW - Exploration process

KW - Feller property

KW - Infinitesimal generator

KW - Lévy snake

KW - Measure valued process

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JF - Journal of Theoretical Probability

IS - 2

ER -

Feller property and infinitesimal generator of the exploration process

Abstract

Keywords

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