English
Related papers

Related papers: Statistical inference for discretely sampled stoch…

200 papers

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of…

Probability · Mathematics 2011-11-10 Andreas Neuenkirch , Samy Tindel

We derive the strong consistency of the least squares estimator for the drift coefficient of a fractional stochastic differential system. The drift coeffcient is one-sided dissipative Lipschitz and the driving noise is additive and…

Probability · Mathematics 2018-03-06 Yaozhong Hu , David Nualart , Hongjuan Zhou

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…

Statistics Theory · Mathematics 2017-10-16 Trisha Maitra , Sourabh Bhattacharya

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

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

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

Machine Learning · Statistics 2020-06-29 Martin Jørgensen , Marc Peter Deisenroth , Hugh Salimbeni

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…

Machine Learning · Computer Science 2019-05-29 Gabriele Abbati , Philippe Wenk , Michael A Osborne , Andreas Krause , Bernhard Schölkopf , Stefan Bauer

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…

Machine Learning · Computer Science 2023-10-05 Victor Chardès , Suryanarayana Maddu , Michael J. Shelley

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

Optimization and Control · Mathematics 2015-04-27 Viorel Barbu , Stefano Bonaccorsi , Luciano Tubaro

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

Probability · Mathematics 2023-05-23 Bixiang Wang

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…

Probability · Mathematics 2014-03-13 Bruno Saussereau

In this paper, we consider a Stochastic Delay Differential Equation with constant delay $r>0$ and, under the same conditions on the coefficients needed to ensure the smoothness of the density plus an ellipticity condition on the diffusion…

Probability · Mathematics 2024-10-22 Òscar Burés , Carles Rovira

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

The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…

Probability · Mathematics 2015-01-06 Alberto Chiarini , Markus Fischer

In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$, two unknown parameters. We suppose that the process is discretely observed at the…

Statistics Theory · Mathematics 2020-11-30 Chiara Amorino , Arnaud Gloter

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…

Probability · Mathematics 2012-04-05 Paul Dupuis , Konstantinos Spiliopoulos

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

Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…

Probability · Mathematics 2017-10-27 David Lipshutz

Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…

Numerical Analysis · Mathematics 2020-07-29 Daxin Nie , Jing Sun , Weihua Deng