Related papers: On a discrete approximation of a skew stable L\'{e…

In this paper we consider a finite state time discrete Markov chain that mimics the behaviour of solutions of the stochastic differential equation $dX=-U'(X)dt+\epsilon dL$, where $U$ is a multi-well potential with $n\geq 2$ local minima…

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…

Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…

In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at…

Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…

As an analogue to the explicit formula in the stable case, the asymptotic behavior at the origin of the renormalized zero resolvent of one-dimensional L\'evy processes is studied under certain regular variation conditions on the…

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…

In this short note we study homogenization of symmetric $d$-dimensional L\'evy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \emph{et al.} in 1992; their motivation was the work by…

The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to…

This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…

We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition probability of a fixed L\'evy process. In analogy to the…

Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…

This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Loewner Evolution (SLE) by Oded…

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…

We obtain an asymptotic H\"older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized…

We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-dimensional L\'evy processes that drifts to plus infinity.…

Let $(X_1, \xi_1), (X_2,\xi_2),\ldots$ be i.i.d.~copies of a pair $(X,\xi)$ where $X$ is a random process with paths in the Skorokhod space $D[0,\infty)$ and $\xi$ is a positive random variable. Define $S_k := \xi_1+\ldots+\xi_k$, $k \in…

For a strictly stationary sequence of random vectors in $\mathbb{R}^d$ we study convergence of partial sum processes to L\'evy stable process in the Skorohod space with $J_1$-topology. We identify necessary and sufficient conditions for…