相关论文: Hitting distributions of alpha-stable processes vi…
In this paper, we continue our understanding of the stable process from the perspective of the theory of self-similar Markov processes in the spirit of the recent papers of Kyprianou (2016) and Kyprianou et al. (2017). In particular, we…
For any two-sided jumping $\alpha$-stable process, where $1 < \alpha < 2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided…
Recent fluctuation identities for $\alpha$-stable L\'evy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
We show that the hitting times for points of real $\alpha-$stable L\'evy processes ($1<\alpha\le 2$) are unimodal random variables. The argument relies on strong unimodality and several recent multiplicative identities in law. In the…
This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…
The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
Around the 1960s a celebrated collection of papers emerged offering a number of explicit identities for the class of isotropic stable processes in one and higher dimensions; these include, for example, the lauded works of Blumenthal,…
The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…
In this paper, we prove two limit laws for functionals of self-intersection symmetric alpha-stable processes with alpha\in(1,2). The results are obtained based on the method of moments, the sample configuration and the chaining argument…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute…
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…
Several aspects of the laws of first hitting times of points are investigated for one-dimensional symmetric stable L\'evy processes. It\^o's excursion theory plays a key role in this study.
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…
In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results,…
Let $A_t$ be an $\alpha$-stable symmetric process, $0<\alpha\leq 2$, on $\mathbb{R}^d$ and $D\subset \mathbb{R}^d$ be a bounded domain. This paper presents a proof, based on the classical Brascamp-Lieb-Luttinger inequalities for multiple…
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…
We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…