Related papers: Low frequency estimation of continuous-time moving…

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…

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right), \] where \(\xi_s\) is a L{\'e}vy process.…

Let $X$ be a $d$-dimensional L\'evy process with L\'evy triplet $(\Sigma,\nu,\alpha)$ and $d\geq 2$. Given the low frequency observations $(X_t)_{t=1,\ldots,n}$, the dependence structure of the jumps of $X$ is estimated. The L\'evy measure…

We consider a mixed moving average (MMA) process X driven by a L\'evy basis and prove that it is weakly dependent with rates computable in terms of the moving average kernel and the characteristic quadruple of the L\'evy basis. Using this…

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…

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…

We consider high-frequency sampled continuous-time autoregressive moving average (CARMA) models driven by finite-variance zero-mean L\'evy processes. An L^2-consistent estimator for the increments of the driving L\'evy process without order…

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 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…

In this paper we present a parametric estimation method for certain multi-parameter heavy-tailed L\'evy-driven moving averages. The theory relies on recent multivariate central limit theorems obtained in [3] via Malliavin calculus on…

We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…

The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…

This paper is devoted to the study of an averaging principle for fractional stochastic differential equations in Rnwith L\'evy motion, using an integral transform method. We obtain a time-averaged equation under suitable assumptions.…

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.…

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…

We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…

We estimate a median of $f(X_t)$ where $f$ is a Lipschitz function, $X$ is a L\'evy process and $t$ an arbitrary time. This leads to concentration inequalities for $f(X_t)$. In turn, corresponding fluctuation estimates are obtained under…

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…

We consider the problem of estimating the density of the process associated with the small jumps of a pure jump L\'evy process, possibly of infinite variation, from discrete observations of one trajectory. The interest of such a question…

The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to…