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Related papers: Estimating a class of diffusions from discrete obs…

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Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…

Machine Learning · Statistics 2023-12-12 Yinuo Ren , Yiping Lu , Lexing Ying , Grant M. Rotskoff

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…

Statistics Theory · Mathematics 2013-08-14 Chenxu Li

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

Data Analysis, Statistics and Probability · Physics 2009-11-13 D. Kleinhans , R. Friedrich

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Statistics Theory · Mathematics 2018-05-30 Shogo H. Nakakita , Masayuki Uchida

For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…

Statistics Theory · Mathematics 2011-11-09 Stefano Iacus , Masayuki Uchida , Nakahiro Yoshida

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…

Statistics Theory · Mathematics 2012-03-12 Jinyuan Chang , Song Xi Chen

Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus…

Statistics Theory · Mathematics 2025-06-27 Eddy Ella-Mintsa

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…

Statistics Theory · Mathematics 2007-09-20 A. De Gregorio , S. M. Iacus

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

We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they…

Statistics Theory · Mathematics 2025-09-30 Mohamed Ben Alaya , Martin Friesen , Jonas Kremer

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Methodology · Statistics 2024-01-30 Yuga Iguchi , Alexandros Beskos , Matthew M. Graham

We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…

Statistics Theory · Mathematics 2025-12-30 Maud Delattre , Hiroki Masuda

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

Probability · Mathematics 2016-09-29 Joscha Diehl , Peter Friz , Hilmar Mai

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Statistics Theory · Mathematics 2007-06-13 Yacine Ait-Sahalia , Per A. Mykland

We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…

Statistics Theory · Mathematics 2020-02-25 Arnaud Gloter , Nakahiro Yoshida

We study the problem of estimating the coefficients of a diffusion (X_t,t\geq 0); the estimation is based on discrete data X_{n\Delta},n=0,1,...,N. The sampling frequency \Delta^{-1} is constant, and asymptotics are taken as the number N of…

Statistics Theory · Mathematics 2007-06-13 Emmanuel Gobet , Marc Hoffmann , Markus Reiss

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

In this article, we consider a jump diffusion process (X_t), with drift function b, diffusion coefficient sigma and jump coefficient xi^{2}. This process is observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends…

Statistics Theory · Mathematics 2013-11-27 Emeline Schmisser

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…

Computation · Statistics 2023-09-20 Elsiddig Awadelkarim , Ajay Jasra , Hamza Ruzayqat

In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…

Methodology · Statistics 2021-08-31 J. L. Kirkby , Dang Nguyen , Duy Nguyen , Nhu Nguyen