scholarly journals Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration

2009 ◽  
Vol 133 (4) ◽  
pp. 355-382 ◽  
Author(s):  
Pierre Patie
Keyword(s):  
Lévy Processes ◽  
Branching Processes ◽  
Levy Processes ◽  
Exponential Functional ◽  
New Family ◽  
Continuous State ◽  
Self Similar

scholarly journals Double hypergeometric Lévy processes and self-similarity

2021 ◽  
Vol 58 (1) ◽  
pp. 254-273
Author(s):  
Andreas E. Kyprianou ◽  
Juan Carlos Pardo ◽  
Matija Vidmar
Keyword(s):  
Closed Form ◽  
Markov Processes ◽  
Lévy Processes ◽  
Levy Processes ◽  
Stable Processes ◽  
Self Similarity ◽  
New Family ◽  
Self Similar

AbstractMotivated by a recent paper (Budd (2018)), where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Lévy processes, called the double hypergeometric class, whose Wiener–Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.

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}.

scholarly journals Continuous-State Branching Processes and Self-Similarity

2008 ◽  
Vol 45 (04) ◽  
pp. 1140-1160 ◽  
Author(s):  
A. E. Kyprianou ◽  
J. C. Pardo
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
Self Similarity ◽  
Lamperti Transformation ◽  
Continuous State ◽  
Self Similar

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.

scholarly journals Apparent multifractality of self-similar Lévy processes

Nonlinearity ◽  
2017 ◽  
Vol 30 (7) ◽  
pp. 2592-2611
Author(s):  
Marco Zamparo
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Self Similar

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
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