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From nonparametric regression to statistical inference for non-Ergodic diffusion processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	From nonparametric regression to statistical inference for non-Ergodic diffusion processes by Nicolas Marie.
Author:	Marie, Nicolas.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xii, 184 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Stochastic differential equations.
Online resource:	https://doi.org/10.1007/978-3-031-95638-6
ISBN:	9783031956386$q(electronic bk.)

From nonparametric regression to statistical inference for non-Ergodic diffusion processes
Marie, Nicolas.

From nonparametric regression to statistical inference for non-Ergodic diffusion processes [electronic resource] /by Nicolas Marie. - Cham :Springer Nature Switzerland :2025. - xii, 184 p. :ill., digital ;24 cm. - Frontiers in probability and the statistical sciences,2624-9995. - Frontiers in probability and the statistical sciences..

Introduction -- Nonparametric regression: a detailed reminder -- The projection least squares estimator of the drift function -- Going further with the projection least squares method: diffusions with jumps and fractional diffusions -- The Nadaraya-Watson estimator of the drift function.

This book is about copies-based nonparametric estimation of the drift function in stochastic differential equations (SDEs) driven by Brownian motion, a jump process, or fractional Brownian motion. While the estimators of the drift function in SDEs are classically computed from one long-time observation of the ergodic stationary solution, here the estimation framework - which is part of functional data analysis - involves multiple copies of the (non-stationary) solution observed over a short-time interval. Two kinds of nonparametric estimators are investigated for SDE models, first presented in the regression framework: the projection least squares estimator and the Nadaraya-Watson estimator. Adaptive procedures are provided for possible applications in statistical learning. Primarily intended for researchers in statistical inference for stochastic processes who are interested in the copies-based observation scheme, the book will also be useful for graduate and PhD students in probability and statistics, thanks to its multiple reminders of the requisite theory, especially the chapter on nonparametric regression.

ISBN: 9783031956386$q(electronic bk.)

Standard No.: 10.1007/978-3-031-95638-6doiSubjects--Topical Terms:

185784
Stochastic differential equations.

LC Class. No.: QA274.23 / .M37 2025

Dewey Class. No.: 519.22

From nonparametric regression to statistical inference for non-Ergodic diffusion processes
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520 $a This book is about copies-based nonparametric estimation of the drift function in stochastic differential equations (SDEs) driven by Brownian motion, a jump process, or fractional Brownian motion. While the estimators of the drift function in SDEs are classically computed from one long-time observation of the ergodic stationary solution, here the estimation framework - which is part of functional data analysis - involves multiple copies of the (non-stationary) solution observed over a short-time interval. Two kinds of nonparametric estimators are investigated for SDE models, first presented in the regression framework: the projection least squares estimator and the Nadaraya-Watson estimator. Adaptive procedures are provided for possible applications in statistical learning. Primarily intended for researchers in statistical inference for stochastic processes who are interested in the copies-based observation scheme, the book will also be useful for graduate and PhD students in probability and statistics, thanks to its multiple reminders of the requisite theory, especially the chapter on nonparametric regression.
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