Related papers: Nonparametric estimation of the characteristic tri…
Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
This paper is concerned with nonparametric estimation of the L\'evy density of a pure jump L\'evy process. The sample path is observed at $n$ discrete instants with fixed sampling interval. We construct a collection of estimators obtained…
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…
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
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…
In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$…
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…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
Efficient estimation of a non-Gaussian stable Levy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a…
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. First, we provide results that give upper estimates in a situation when the corresponding jump measure is allowed to be highly…
In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $\beta$-stable L\'evy processes, $\beta \in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of…
In this paper, we study the nonparametric estimation of the density $f_\Delta$ of an increment of a L\'evy process $X$ based on $n$ observations with a sampling rate $\Delta$. The class of L\'evy processes considered is broad, including…
We consider a recurrent Markov process which is an It\^o semi-martingale. The L\'evy kernel describes the law of its jumps. Based on observations X(0),X({\Delta}),...,X(n{\Delta}), we construct an estimator for the L\'evy kernel's density.…
Existing results for the estimation of the L\'evy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional L\'evy processes in order to construct a nonparametric estimator for the…
In this paper nonparametric methods to assess the multivariate L\'{e}vy measure are introduced. Starting from high-frequency observations of a L\'{e}vy process $\mathbf{X}$, we construct estimators for its tail integrals and the…
We establish the global asymptotic equivalence between a pure jumps L\'evy process $\{X_t\}$ on the time interval $[0,T]$ with unknown L\'evy measure $\nu$ belonging to a non-parametric class and the observation of $2m^2$ Poisson…
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…
We study the nonparametric calibration of exponential L\'{e}vy models with infinite jump activity. In particular our analysis applies to self-decomposable processes whose jump density can be characterized by the $k$-function, which is…