Related papers: Estimating the input of a L\'evy-driven queue by P…
This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every…
We consider a supercritical branching L\'evy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit theorem on the empirical mean position.
In this paper we study the problem of constructing bootstrap confidence intervals for the L\'evy density of the driving L\'evy process based on high-frequency observations of a L\'evy-driven moving average processes. Using a spectral…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
We establish explicit quenched asymptotics for pure-jump symmetric L\'evy processes in general Poissonian potentials, which is closely related to large time asymptotic behavior of solutions to the nonlocal parabolic Anderson problem with…
A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a L\'evy process in a metrizable compact group to be asymptotically uniform with probability one.
We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species…
Although introduced in the case of Poisson random measures, the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…
The estimation of the L\'{e}vy density, the infinite-dimensional parameter controlling the jump dynamics of a L\'{e}vy process, is considered here under a discrete-sampling scheme. In this setting, the jumps are latent variables, the…
We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…
Intermittent demand fluctuations pose significant challenges in disaster logistics and medical supply systems. In this study, we formulate cumulative demand as a generalized L\'evy process composed of a drift term, Poisson jumps, and…
In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…
By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…