scholarly journals Recurrent extensions of self-similar Markov processes and Cramér’s condition II

Bernoulli ◽  
2007 ◽  
Vol 13 (4) ◽  
pp. 1053-1070 ◽  
Author(s):  
Víctor Rivero
Keyword(s):  
Markov Processes ◽  
Cramér’S Condition ◽  
Self Similar

A temporal factorization at the maximum for certain positive self-similar Markov processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Absorption Time ◽  
The Laplace Transform ◽  
Self Similar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

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 Recurrent Extensions of Real-Valued Self-Similar Markov Processes

2019 ◽  
Vol 53 (3) ◽  
pp. 899-920 ◽  
Author(s):  
H. Pantí ◽  
J. C. Pardo ◽  
V. M. Rivero
Keyword(s):  
Markov Processes ◽  
Self Similar

scholarly journals Fluctuation theory and exit systems for positive self-similar Markov processes

2012 ◽  
Vol 40 (1) ◽  
pp. 245-279 ◽  
Author(s):  
Loïc Chaumont ◽  
Andreas Kyprianou ◽  
Juan Carlos Pardo ◽  
Víctor Rivero
Keyword(s):  
Markov Processes ◽  
Fluctuation Theory ◽  
Self Similar

scholarly journals On some transformations between positive self-similar Markov processes

2007 ◽  
Vol 117 (12) ◽  
pp. 1889-1909 ◽  
Author(s):  
Loïc Chaumont ◽  
Víctor Rivero
Keyword(s):  
Markov Processes ◽  
Self Similar
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