Related papers: Fluctuation theory for L\'evy processes with compl…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
Assume that $g(|\xi|^2)$, $\xi\in\mathbb{R}^k$, is for every dimension $k\in\mathbb{N}$ the characteristic function of an infinitely divisible random variable $X^k$. By a classical result of Schoenberg $f:=-\log g$ is a Bernstein function.…
We present a numerical scheme to calculate fluctuation identities for exponential L\'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult…
We consider the class of (possibly killed) spectrally positive L\'evy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following…
We study the symmetry of large deviation functions associated with time-integrated currents in Markov pure jump processes. One current known to have this symmetry is the fluctuating entropy production and this is the content of the…
We establish a new connection between the class of Nevanlinna-Pick functions and the one of the exponents associated to spectrally negative L\'evy processes. As a consequence, we compute the characteristics related to some hyperbolic…
Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular,…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
We consider here point processes $N^f(t)$, $t>0$, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bern\v{s}tein functions $f$ with L\'evy measure $\nu$. We obtain the general expression of…
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…
In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are…
We prove a fluctuating limit theorem of a sequence of super-Brownian motions over $\mbb{R}$ with a single point catalyst. The weak convergence of the processes on the space of Schwarz distributions is established. The limiting process is an…
The optimal stopping problem for a Hunt processes on $\R$ is considered via the representation theory of excessive functions. In particular, we focus on infinite horizon (or perpetual) problems with one-sided structure, that is, there…
Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Levy process Z above a positive level a. In this paper it is shown that the law of T(a) can be approximated arbitrarily closely by the laws of…
We consider a new class of determinantal point processes in the complex plane coming from the ground state of free fermions associated with Berezin--Toeplitz operators. These processes generalize the Ginibre ensemble from random matrix…
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…