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2007 Branching diffusions, superdiffusions and random media
János Engländer
Probab. Surveys 4: 303-364 (2007). DOI: 10.1214/07-PS120

Abstract

Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinear partial differential equations. Another hot topic in today’s research in probability theory is ‘random media’, including the now classical problems on ‘Brownian motion among obstacles’ and the more recent ‘random walks in random environment’ and ‘catalytic branching’ models. These notes aim to give a gentle introduction into some topics in spatial branching processes and superprocesses in deterministic environments (sections 2-6) and in random media (sections 7-11).

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János Engländer. "Branching diffusions, superdiffusions and random media." Probab. Surveys 4 303 - 364, 2007. https://doi.org/10.1214/07-PS120

Information

Published: 2007
First available in Project Euclid: 16 January 2008

zbMATH: 1189.60143
MathSciNet: MR2368953
Digital Object Identifier: 10.1214/07-PS120

Subjects:
Primary: 60J60
Secondary: 60J80

Keywords: Branching diffusions , Catalytic branching , compact support property , criticality theory , Law of Large Numbers , Local extinction , Measure-valued processes , mild obstacles , nonlinear h-transform , random environment , Random media , second order elliptic operators , Spatial branching processes , spine decomposition , Superprocesses

Rights: Copyright © 2007 The Institute of Mathematical Statistics and the Bernoulli Society

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