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Seminar by Department of Discrete Mathematic, Steklov Mathematical Institute of RAS
June 7, 2018 16:00, Moscow, Steklov Mathematical Institute of RAS, Room 511 (8 Gubkina)
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Extinction rate of continuous state branching processes in critical Lévy random environments
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Abstract:
We determine the speed of extinction of continuous state branching
processes (CSBPs) in an oscillating Lévy random environment satisfying
the so-called Spitzer's condition. The study relies on the path analysis
of the process together with its environment, conditionally on the
survival event, following the approach for discrete time branching
processes in random environment of Afanasyev et al. [1]. In particular,
we characterize CSBPs in a random environment conditioned to stay
positive as a solution of a stochastic differential equation and
determine its long time behavior.
This is a joint work with Vincent Bansaye (CMAP, Ecole Polytechnique) and Juan Carlos Pardo (CIMAT).
Keywords:
branching processes, Random environment, Lévy processes.
Language: English
References
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Afanasyev V.I., Geiger J., Kersting G. and Vatutin V.A., “Criticality for branching processes in random environment”, Ann. Probab., 33:2 (2005), 645–673
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