Related papers: Optimal convergence rates for the invariant densit…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
In this paper, we consider a symmetric pure jump Markov process $X$ on a metric measure space with volume doubling conditions. Our focus is on estimating the transition density $p(t,x,y)$ of $X$ and studying its stability when the jumping…
Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…
We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous Poisson random measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with…
The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous It\^{o} semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the…
We consider estimation of a step function $f$ from noisy observations of a deconvolution $\phi*f$, where $\phi$ is some bounded $L_1$-function. We use a penalized least squares estimator to reconstruct the signal $f$ from the observations,…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
We study the problem of the non-parametric estimation for the density $\pi$ of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the continuous…
Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as…
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…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
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…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which…
We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of…
An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between the intensity of jumps and the speed of…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…