Related papers: Sup-norm adaptive simultaneous drift estimation fo…

We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…

This paper studies the theoretical underpinnings of machine learning of ergodic It\^o diffusions. The objective is to understand the convergence properties of the invariant statistics when the underlying system of stochastic differential…

The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…

We consider the adaptive test for the parameter change in discretely observed ergodic diffusion processes based on the cusum test. Using two test statistics based on the two quasi-log likelihood functions of the diffusion parameter and the…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…

In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and…

We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

We derive uniform concentration inequalities for continuous-time analogues of empirical processes and related stochastic integrals of scalar ergodic diffusion processes. Thereby, we lay the foundation typically required for the study of…

We consider the problem of nonparametric estimation of the drift of a continuously observed one-dimensional diffusion with periodic drift. Motivated by computational considerations, van der Meulen e.a. (2014) defined a prior on the drift as…

We aim at estimating the invariant density associated to a stochastic differential equation with jumps in low dimension, which is for $d=1$ and $d=2$. We consider a class of jump diffusion processes whose invariant density belongs to some…

We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the rate of convergence to equilibrium is maximized. We solve…

We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian…

We consider the setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…

The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estimator generalizes the spectral method by Gobet, Hoffmann and…

We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…

A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypotheses…