scholarly journals A hitting time for Lévy processes, with application to dams and branching processes

1996 ◽  
Vol 5 (3) ◽  
pp. 521-544 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Lévy Processes ◽  
Branching Processes ◽  
Levy Processes ◽  
Hitting Time

scholarly journals Branching processes in Lévy processes: the exploration process

1998 ◽  
Vol 26 (1) ◽  
pp. 213-252 ◽  
Author(s):  
Jean-Francois Le Gall ◽  
Yves Le Jan
Keyword(s):  
Lévy Processes ◽  
Branching Processes ◽  
Levy Processes ◽  
Exploration Process

scholarly journals Extinction rate of continuous state branching processes in critical Lévy environments

2021 ◽  
Author(s):  
Juan Carlos Pardo ◽  
Vincent Bansaye ◽  
Charline Smadi
Keyword(s):  
Lévy Process ◽  
Lévy Processes ◽  
Branching Process ◽  
Branching Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Extinction Rate ◽  
Exponential Moments ◽  
Continuous State ◽  
Remarkable Result

We study  the  speed  of extinction of continuous state branching processes in a Lévy environment, where the associated Lévy process oscillates.  Assuming that the  Lévy process satisfies  Spitzer's condition and the existence of some  exponential moments, we extend recent results where the associated branching mechanism is stable. The study  relies on the  path analysis of  the branching process  together with its Lévy environment, when the latter is conditioned to have a non negative running infimum. For that purpose,  we combine the  approach  developed in    Afanasyev et al. \cite{Afanasyev2005},  for the discrete setting and i.i.d. environments, with fluctuation theory of Lévy processes and a remarkable result on exponential functionals of Lévy processes under Spitzer's condition due to Patie and Savov \cite{patie2016bernstein}.

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