Related papers: Infinitesimal generators for two-dimensional L\'ev…
We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…
The law of a positive infinitely divisible process with no drift is characterized by its L\'evy measure on the paths space. Based on recent results of the two authors, it is shown that even for simple examples of such processes, the…
We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We investigate the spectrum of the generator of a self-adjoint transition semigroup of a (symmetric) L\'{e}vy process taking values in $d$--dimensional space.
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic…
We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…
The extraction of nonstationary signals from blind and semi-blind multivariate observations is a recurrent problem. Numerous algorithms have been developed for this problem, which are based on the exact or approximate joint diagonalization…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
For a L\'evy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval $(r,\infty)$, the sojourn time in the interval $(-\infty,r]$, and the last exit time…
In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_{X,Y}(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem. Under these circumstances, we…
We obtain general lower estimates of transition densities of jump L\'evy processes. We use them for processes with L\'evy measures having bounded support, processes with exponentially decaying L\'evy measures for large times and for…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its L\'evy measure and the tail equivalence between the density and its…