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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes (Frontiers in Probability and the Statistical Sciences) - Hardcover
Synopsis
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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About the Author
Nicolas Marie is an associate professor in the Modal’X department at Paris Nanterre University. He received his PhD in probability in 2012, and his habilitation in statistics and probability in 2019. First, in the rough paths theory framework, he focused on constrained fractional diffusions. Then, since 2017, Nicolas Marie contributes to investigate the copies-based statistical inference for diffusions and fractional diffusions.
From the Back Cover
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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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes (eng)
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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
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ISBN 10: 3031956370
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 184 pp. Englisch. Seller Inventory # 9783031956379
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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
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ISBN 13: 9783031956379
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783031956379
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From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
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Springer, Birkhäuser Sep 2025, 2025
ISBN 10: 3031956370
ISBN 13: 9783031956379
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Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 196 pp. Englisch. Seller Inventory # 9783031956379
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