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Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

Statistical Mechanics · Physics 2023-05-10 Johan du Buisson , Hugo Touchette

A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk.…

Statistics Theory · Mathematics 2015-09-21 L. I. Galtchouk , S. M. Pergamenshchikov

In this paper, we investigate the parameter estimation for threshold Ornstein$\mathit{-}$Uhlenbeck processes. Least squares method is used to obtain continuous-type and discrete-type estimators for the drift parameters based on continuous…

Statistics Theory · Mathematics 2024-03-28 Yuecai Han , Dingwen Zhang

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our…

Statistical Finance · Quantitative Finance 2009-11-06 Aleksandar Mijatovic , Paul Schneider

We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…

Statistics Theory · Mathematics 2018-07-04 Theodoros Manikas , Anastasia Papavasiliou

Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…

Statistics Theory · Mathematics 2008-12-18 Ismael Castillo , Jean-Michel Loubes

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…

Statistics Theory · Mathematics 2019-02-04 Frank van der Meulen , Moritz Schauer , Jan van Waaij

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

Statistics Theory · Mathematics 2017-05-29 Forzani Liliana , Fraiman Ricardo , Llop Pamela

We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems for continuous…

Machine Learning · Statistics 2026-05-19 Sunia Tanweer , Firas A. Khasawneh

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction…

Statistics Theory · Mathematics 2019-12-02 Boualem Djehiche , Othmane Mazhar , Cristian R. Rojas

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Machine Learning · Statistics 2024-11-05 Luc Brogat-Motte , Riccardo Bonalli , Alessandro Rudi

The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…

Statistics Theory · Mathematics 2007-06-13 Arnak Dalalyan

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…

Statistics Theory · Mathematics 2009-08-14 Paul Malliavin , Maria Elvira Mancino

We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new…

Statistics Theory · Mathematics 2015-12-29 Yohann De Castro , Élisabeth Gassiat , Claire Lacour

This paper explores the nonparametric estimation of the volatility component in a heteroscedastic scalar-on-function regression model, where the underlying discrete-time process is ergodic and subject to a missing-at-random mechanism. We…

Methodology · Statistics 2024-12-17 Abdelbasset Djeniah , Mohamed Chaouch , Amina Angelika Bouchentouf

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…

Statistics Theory · Mathematics 2017-03-17 Yasutaka Shimizu

This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…

Statistics Theory · Mathematics 2020-09-17 Maud Delattre

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

Statistics Theory · Mathematics 2018-08-21 Miljenko Huzak

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…

Statistics Theory · Mathematics 2020-06-02 Carsten Chong