Related papers: Estimating the input of a L\'evy-driven queue by P…
This paper focuses on hypothesis testing for the input of a L\'evy-driven storage system by sampling of the storage level. As the likelihood is not explicit we propose two tests that rely on transformation of the data. The first approach…
Our goal is to estimate the characteristic exponent of the input to a L\'evy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the…
In this paper we analyze the transient behavior of the workload process in a L\'evy input queue. We are interested in the value of the workload process at a random epoch; this epoch is distributed as the sum of independent exponential…
Estimation methods for the L\'{e}vy density of a L\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good…
We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax…
We propose a novel estimation framework for path-dependent functionals of Levy processes from discretely observed data. Traditional approaches rely on Monte Carlo simulation of full paths, which requires complete model specification and…
In this paper we study a queue with L\'evy input, without imposing any a priori assumption on the jumps being one-sided. The focus is on computing the transforms of all sorts of quantities related to the transient workload, assuming the…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form $$Z_{t} = \int_{\mathbb{R}}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}$$ with a deterministic kernel (\K\) and a…
We introduce two types of estimators of the finite-dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and multi-step MLE. It is shown that the estimators…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…
This study examines a nonparametric inference on a stationary L\'evy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the L\'evy measure of the…
In this article we consider L\'evy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample…
We address estimation of parametric coefficients of a pure-jump L\'evy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study Masuda…
In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…