The law of the hitting times to points by a stable Lev́y process with no negative jumps.

Peskir, Goran

Displaying similar documents to “The law of the hitting times to points by a stable Lev́y process with no negative jumps.”

Two-sided exit problem for a spectrally negative $α$ -stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions.

Patie, Pierre (2007)

Electronic Communications in Probability [electronic only]

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Penalisation of a stable Lévy process involving its one-sided supremum

Kouji Yano, Yuko Yano, Marc Yor (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Penalisation involving the one-sided supremum for a stable Lévy process with index ∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.

A Ciesielski–Taylor type identity for positive self-similar Markov processes

A. E. Kyprianou, P. Patie (2011)

Annales de l'I.H.P. Probabilités et statistiques

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The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical...

Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes

Patie Pierre (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We first characterize the increasing eigenfunctions associated to the following family of integro-differential operators, for any , >0, ≥0 and a smooth function on $ℜ^{+}$ , $\begin{matrix} 𝐋^{(γ)} f (x) = x^{- α} (\frac{σ}{2} x^{2} f^{''} (x) + (σ γ + b) x f^{'} (x) \\ + \int_{0}^{\infty} (f (e^{- r} x) - f (x)) e^{- r γ} + x f^{'} (x) r 𝕀_{{r \leq 1}} ν (d r)), (0.1) \end{matrix}$ where the coefficients $b \in ℜ$ ,≥0 and the measure , which satisfies the integrability condition (1∧ )(d)<+∞, are uniquely determined by the distribution of a spectrally negative, infinitely divisible random variable, with characteristic exponent . ...

Small time expansions for transition probabilities of some Lev́y processes.

Marchal, Philippe (2009)

Electronic Communications in Probability [electronic only]

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

Anthony G. Pakes (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct.

Lambert, Amaury (2007)

Electronic Journal of Probability [electronic only]

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The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation

Gerónimo Uribe Bravo (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We present a further analysis of the fragmentation at heights of the normalized brownian excursion. Specifically we study a representation for the mass of a tagged fragment in terms of a Doob transformation of the 1/2-stable subordinator and use it to study its jumps; this accounts for a description of how a typical fragment falls apart. These results carry over to the height fragmentation of the stable tree. Additionally, the sizes of the fragments in the brownian height fragmentation...