Related papers: Stable L\'evy processes in a cone
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…
We consider some special classes of L\'evy processes with no gaussian component whose L\'evy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1) dx$, where $\nu$ is the density of the stable L\'evy measure and $\gamma$ is a positive…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
Let X be a critical branching L{\'e}vy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different…
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the…
In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…
Markov-modulated L\'evy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions…
We compute the persistence exponent of the integral of a stable L\'evy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Z. Shi (2003). Along the way, we investigate the law of the stable…
Iksanov and Pilipenko (2023) defined a skew stable L\'{e}vy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable L\'{e}vy processes (continuous-time processes). Here, we provide a simpler construction of the skew…
Let $X=(X_t, t\geq 0)$ be a self-similar Markov process taking values in $\mathbb{R}$ such that the state 0 is a trap. In this paper, we present a necessary and sufficient condition for the existence of a self-similar recurrent extension of…
This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of…
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of…
Multistable distributions, which have been introduced recently by Falconer, L\'evy V\'ehel and their co-authors, are natural generalizations of symmetric "alpha" stable distributions; roughly speaking, they are obtained by replacing the…
In this paper we introduce a new class of L\'evy processes which we call hypergeometric-stable L\'evy processes, because they are obtained from symmetric stable processes through several transformations and where the Gauss hypergeometric…
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…
We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of…
We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show…
This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
The Lamperti--Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, there is a Markov additive process (MAP). In the case that the rssMp is taken to…