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We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

Machine Learning · Statistics 2026-02-23 Marcos Tapia Costa , Nikolas Kantas , George Deligiannidis

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…

Machine Learning · Computer Science 2023-10-31 Alessio Mazzetto , Eli Upfal

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…

Probability · Mathematics 2018-05-31 Arnab Ganguly , P. Sundar

In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general…

Statistics Theory · Mathematics 2025-10-09 Chiara Amorino , Francisco Pina , Mark Podolskij

We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…

Probability · Mathematics 2019-08-22 Antoine Lejay , Paolo Pigato

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…

Statistics Theory · Mathematics 2009-09-29 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…

Methodology · Statistics 2025-09-26 Miguel Alvarez , Ajay Jasra

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…

Statistics Theory · Mathematics 2026-03-31 Chiara Amorino , Vytautė Pilipauskaitė

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…

Statistics Theory · Mathematics 2011-11-10 Yury A. Kutoyants , Nakahiro Yoshida

We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…

Statistics Theory · Mathematics 2020-04-10 Jean-Charles Croix , Masoumeh Dashti , Istvàn Zoltàn Kiss

We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…

Statistics Theory · Mathematics 2018-06-19 Yury A. Kutoyants

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…

Statistics Theory · Mathematics 2013-09-27 Emeline Schmisser

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

Statistics Theory · Mathematics 2020-02-26 Gregor Pasemann , Wilhelm Stannat

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…

Statistics Theory · Mathematics 2020-10-28 Shogo H Nakakita , Masayuki Uchida

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Machine Learning · Statistics 2017-08-09 Constantino A. García , Abraham Otero , Paulo Félix , Jesús Presedo , David G. Márquez

We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric…

Statistics Theory · Mathematics 2019-11-05 Charlotte Dion , Sarah Lemler

In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are…

Statistics Theory · Mathematics 2025-11-18 Fabienne Comte , Nicolas Marie

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Probability · Mathematics 2021-05-26 Xi Chen , Ilya Timofeyev

We consider a diffusion $(\xi_t)_{t\ge 0}$ with some $T$-periodic time dependent input term contained in the drift: under an unknown parameter $\vth\in\Theta$, some discontinuity - an additional periodic signal - occurs at times…

Statistics Theory · Mathematics 2010-03-18 Reinhard Hoepfner , Yury Kutoyants

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Methodology · Statistics 2017-04-03 Nina Munkholt Jakobsen , Michael Sørensen