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We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Duquesne and Le Gall, with an underlying Poisson process, we construct a…

Probability · Mathematics 2007-05-23 Romain Abraham , Jean-Francois Delmas

We consider the exponential functional $A_{\infty}=\int_0^{\infty} e^{\xi_s} ds$ associated to a Levy process $(\xi_t)_{t \geq 0}$. We find the asymptotic behavior of the tail of this random variable, under some assumptions on the process…

Probability · Mathematics 2007-05-23 Mejane Olivier

Suppose Xt is either a regular exponential type Levy process or a Levy process with a bounded variation jumps measure. The distribution of the extrema of Xt play a crucial role in many financial and actuarial problems. This article employs…

Probability · Mathematics 2017-01-23 Amir T. Payandeh Najafabadi , Dan Kucerovsky

We consider a class of L\'evy-type processes on which spectral analysis technics can be made to produce optimal results, in particular for the decay rate of their survival probability and for the spectral gap of their ground state…

Probability · Mathematics 2023-06-30 Grégoire Véchambre

We prove a new rearrangement inequality for multiple integrals, which partly generalizes a result of Friedberg and Luttinger (1976) and can be interpreted as involving symmetric rearrangements of domains around infinity. As applications, we…

Probability · Mathematics 2013-02-06 Alexander Drewitz , Perla Sousi , Rongfeng Sun

The LAN property is proved in the statistical model based on discrete-time observations of a solution to a L\'{e}vy driven SDE. The proof is based on a general sufficient condition for a statistical model based on a discrete observations of…

Statistics Theory · Mathematics 2014-04-08 Dmytro Ivanenko , Alexey Kulik

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…

Statistical Mechanics · Physics 2009-10-31 Rudolf Gorenflo , Gianni De Fabritiis , Francesco Mainardi

We present a class of L\'evy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated L\'evy…

Probability · Mathematics 2025-11-21 Uwe Küchler , Stefan Tappe

Trawl processes belong to the class of continuous-time, strictly stationary, infinitely divisible processes; they are defined as Levy bases evaluated over deterministic trawl sets. This article presents the first nonparametric estimator of…

Statistics Theory · Mathematics 2026-02-17 Orimar Sauri , Almut E. D. Veraart

We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic…

Probability · Mathematics 2010-12-06 Alexey Kuznetsov , Juan Carlos Pardo

We develop an approach to Malliavin calculus for L\'evy processes from the perspective of expressing a random variable $Y$ by a functional $F$ mapping from the Skorohod space of c\`adl\`ag functions to $\mathbb{R}$, such that $Y=F(X)$ where…

Probability · Mathematics 2014-10-31 Alexander Steinicke

In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural…

Methodology · Statistics 2018-02-20 Stepan Mazur , Dmitry Otryakhin , Mark Podolskij

We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that…

Number Theory · Mathematics 2023-03-21 Philippe Lebacque , Kohji Matsumoto , Masahiro Mine , Yumiko Umegaki

In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…

Probability · Mathematics 2025-11-25 Max Nendel

Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for…

Probability · Mathematics 2007-05-23 P. J. Fitzsimmons

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences…

Statistical Mechanics · Physics 2018-06-11 Vincent Wens

Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner evolution (SLE) where the branching is possible in a course of growth process. We consider a class of radial Levy-Loewner evolutions for which sets of points of the…

Mathematical Physics · Physics 2019-02-26 Igor Loutsenko , Oksana Yermolayeva

The one dimensional distribution of a L\'{e}vy process is not known in general even though its characteristic function is given by the famous L\'{e}vy-Khinchine theorem. This article gives an exact series representation for the one…

Probability · Mathematics 2008-09-15 Heikki J. Tikanmäki

The characteristic measure of excursions away from a regular point is studied for a class of symmetric L\'evy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result…

Probability · Mathematics 2009-09-01 Kouji Yano

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…

Probability · Mathematics 2015-02-20 Luc Rey-Bellet , Konstantinos Spiliopoulos