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CONTINUOUSSTATE BRANCHING PROCESSES AND SELFSIMILARITY
 APPLIED PROBABILITY TRUST (21 OCTOBER 2008)
, 2008
"... In this paper we study the αstable continuousstate branching processes (for α ∈ (1, 2]) and the latter process conditioned never to become extinct in the light of positive selfsimilarity. Understanding the interaction of the Lamperti transformation for continuous state branching processes and the ..."
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Cited by 12 (3 self)
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In this paper we study the αstable continuousstate branching processes (for α ∈ (1, 2]) and the latter process conditioned never to become extinct in the light of positive selfsimilarity. Understanding the interaction of the Lamperti transformation for continuous state branching processes and the Lamperti transformation for positive selfsimilar Markov processes gives access to a number of explicit results concerning the paths of αstable continuousstate branching processes and αstable continuousstate branching processes conditioned never to become extinct.
The extended hypergeometric class of Lévy processes
, 2013
"... With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo [17]. We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. F ..."
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Cited by 1 (0 self)
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With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo [17]. We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.
Selfsimilar Markov processes
"... Abstract: This note surveys some recent results on selfsimilar Markov processes. Since the research around the topic has been very rich during the last fifteen years we do not pretend to cover all the recent developments in the field, and hence we focus mainly in giving a panorama of the areas whe ..."
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Abstract: This note surveys some recent results on selfsimilar Markov processes. Since the research around the topic has been very rich during the last fifteen years we do not pretend to cover all the recent developments in the field, and hence we focus mainly in giving a panorama of the areas where the authors have made contributions.
On the rate of growth of Lévy processes with no positive jumps conditioned to stay positive
, 2007
"... ..."
Applied Probability Trust (20 October 2008) CONTINUOUSSTATE BRANCHING PROCESSES AND SELFSIMILARITY
"... In this paper we study the αstable continuousstate branching processes (for α ∈ (1, 2]) and the latter process conditioned never to become extinct in the light of positive selfsimilarity. Understanding the interaction of the Lamperti transformation for continuous state branching processes and the ..."
Abstract
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In this paper we study the αstable continuousstate branching processes (for α ∈ (1, 2]) and the latter process conditioned never to become extinct in the light of positive selfsimilarity. Understanding the interaction of the Lamperti transformation for continuous state branching processes and the Lamperti transformation for positive selfsimilar Markov processes gives access to a number of explicit results concerning the paths of αstable continuousstate branching processes and αstable continuousstate branching processes conditioned never to become extinct.
ELECTRONIC COMMUNICATIONS in PROBABILITY ON THE RATE OF GROWTH OF LÉVY PROCESSES WITH NO POS ITIVE JUMPS CONDITIONED TO STAY POSITIVE
, 2008
"... In this note, we study the asymptotic behaviour of Lévy processes with no positive jumps conditioned to stay positive and some related processes. In particular, we establish an integral test for the lower envelope at 0 and at + ∞ and an analogue of Khintchin’s law of the iterated logarithm at 0 and ..."
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In this note, we study the asymptotic behaviour of Lévy processes with no positive jumps conditioned to stay positive and some related processes. In particular, we establish an integral test for the lower envelope at 0 and at + ∞ and an analogue of Khintchin’s law of the iterated logarithm at 0 and at +∞, for the upper envelope of the reflected process at its future infimum. 1 Introduction and main results. Let D denote the Skorokhod space of càdlàg paths with real values and defined on the positive real halfline [0,∞) and P a probability measure defined on D under which ξ will be a realvalued Lévy process with no positive jumps starting from 0 and unbounded variation (the latter assumption is to exclude the case when ξ is the difference of a constant drift and a subordinator).