Displaying similar documents to “Refracted Lévy processes”

On suprema of Lévy processes and application in risk theory

Renming Song, Zoran Vondraček (2008)

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

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Let =− where is a general one-dimensional Lévy process and an independent subordinator. Consider the times when a new supremum of is reached by a jump of the subordinator . We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and drifts to −∞, we decompose the absolute supremum of at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.

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 + , 𝐋 ( γ ) f ( x ) = x - α ( σ 2 x 2 f ' ' ( x ) + ( σ γ + b ) x f ' ( x ) + ∫ 0 ∞ f e - r x - f ( x ) e - r γ + x f ' ( x ) r 𝕀 { r ≤ 1 } ν ( d r ) ) , ( 0 . 1 ) where the coefficients b ∈ 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 . ...

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...

Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)

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

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We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude 1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type...