Entrance from 0+ for increasing semi-stable Markov processes

By Jean Bertoin, María Emilia Caballero. 2002

70 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b7b7f29dee4d5aecab17ce943fe5217292528f90

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Citations in the corpus

Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “The interest in these variables seems to be due to the fact that they appear and play a crucial role in various theoretical and applied contexts such as the spectral theory of some non-reversible Markov semigroups ([61, 60]), the study of random planar maps ([12]), limit theorems of Markov chains ([”
Some explicit identities associated with positive self-similar Markov processes. (2007, background): “One easily checks that ξ↑ satisfies conditions for the weak convergence of (X,Px) given in [3, 4, 9].”
On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable (2001, background): “This note is motivated by several recent works [4, 5, 6, 7, 8] related to the so-called exponential functional I = ∫ ∞”
Exponential functionals of Levy processes (2005, unknown): “without reaching ∞, and it is therefore interesting to obtain sharper information about the asymptotic behavior of Xt as t → ∞. The following result was proved in [14] (see also Bertoin and Caballero [11] in the special case when the L´evy process ξ is a subordinator). Theorem 6 Let Xdenote a self-s”
Recurrent extensions of self-similar Markov processes and Cramér’s condition II (2005, unknown): “Moreover, the expression of the entrance law associated with n should be compared to the entrance law of Bertoin and Caballero [1] and Bertoin and Yor [3] for positive self-similar Markov processes that drift to oo.”
The asymptotic behavior of fragmentation processes (2003, background): “If we set τb = inf { t ≥ 0 : 1/χ(t) > b, then Corollary 5 in [8] entails that for every b > 1, b−ατb is stochastically dominated by the variable ∫ ∞ 0 exp(−αξs)ds.”
Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes (2004, background): “The Annals of Probability 2006, Vol. 34, No. 3, 1012–1034 DOI: 10.1214/009117905000000611 © Institute of Mathematical Statistics, 2006”