Statistical Inference for Ergodic Diffusion Processes

Statistical Inference for Ergodic Diffusion Processes encompasses a wealth of results from over ten years of mathematical literature. It provides a comprehensive overview of existing techniques, and presents - for the first time in book form - many new techniques and approaches. An elementary introduction to the field at the start of the book introduces a class of examples - both non-standard and classical - that reappear as the investigation progresses to illustrate the merits and demerits of the procedures. The statements of the problems are in the spirit of classical mathematical statistics, and special attention is paid to asymptotically efficient procedures. Today, diffusion processes are widely used in applied problems in fields such as physics, mechanics and, in particular, financial mathematics. This book provides a state-of-the-art reference that will prove invaluable to researchers, and graduate and postgraduate students, in areas such as financial mathematics, economics, physics, mechanics and the biomedical sciences.
From the reviews:
"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature...It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints...I have no doubt that it will come to be regarded as a classic text." Journal of the Royal Statistical Society, Series A, v. 167

List of contents

1 Diffusion Processes and Statistical Problems.- 2 Parameter Estimation.- 3 Special Models.- 4 Nonparametric Estimation.- 5 Hypotheses Testing.- Historical Remarks.- References.

Summary

Statistical Inference for Ergodic Diffusion Processes encompasses a wealth of results from over ten years of mathematical literature. It provides a comprehensive overview of existing techniques, and presents - for the first time in book form - many new techniques and approaches. An elementary introduction to the field at the start of the book introduces a class of examples - both non-standard and classical - that reappear as the investigation progresses to illustrate the merits and demerits of the procedures. The statements of the problems are in the spirit of classical mathematical statistics, and special attention is paid to asymptotically efficient procedures. Today, diffusion processes are widely used in applied problems in fields such as physics, mechanics and, in particular, financial mathematics. This book provides a state-of-the-art reference that will prove invaluable to researchers, and graduate and postgraduate students, in areas such as financial mathematics, economics, physics, mechanics and the biomedical sciences.

From the reviews:

"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature...It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints...I have no doubt that it will come to be regarded as a classic text." Journal of the Royal Statistical Society, Series A, v. 167

Additional text

From the reviews:

"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature...It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints...I have no doubt that it will come to be regarded as a classic text." Journal of the Royal Statistical Society, Series A, v. 167

"This book is an amazing collection of results and examples of inference problems in the setup considered. Each chapter also considers historical remarks and starts with a very focused introduction explaining in a few lines the content of the chapter. … The book is well written … . This book will be useful to both Ph.D. students in mathematical statistics and young researchers. Experts in the field will also find this collection of results valuable. A must have!" (Stefano Maria Iacus, Mathematical Reviews, 2006 b)

"The author has done a thorough job ofpresenting all that is known in the area of large sample theory of estimation in diffusions processes. Many deep and technically difficult results of the authors and his collaborators appear in the book. A must have for anyone interested in inference in diffusions." (Arup Bose, Sankhya: The Indian Journal of Statistics, Vol. 67 (1), 2005)

"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature. … It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints. The book will be of greatest use to mathematical statisticians, and as a reference work for those highly mathematical financial analysts who are involved in pricing, monitoring and trading derivatives. … I have no doubt that it will come to be regarded as a classic text." (Mohamed Afzal Norat, Journal of the Royal Statistical Society, Vol. 167 (4), 2004)

"This work is a continuation of the study of large sample theory of continuous time stochastic processes investigated by the author … . The book is written in a very clear style and is of use for research workers in the area of stochastic processes." (B. L. S. Prakasa Rao, Zentralblatt MATH, Vol. 1038 (13), 2004)

Report

From the reviews:
"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature...It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints...I have no doubt that it will come to be regarded as a classic text." Journal of the Royal Statistical Society, Series A, v. 167
"This book is an amazing collection of results and examples of inference problems in the setup considered. Each chapter also considers historical remarks and starts with a very focused introduction explaining in a few lines the content of the chapter. ... The book is well written ... . This book will be useful to both Ph.D. students in mathematical statistics and young researchers. Experts in the field will also find this collection of results valuable. A must have!" (Stefano Maria Iacus, Mathematical Reviews, 2006 b)
"The author has done a thorough job ofpresenting all that is known in the area of large sample theory of estimation in diffusions processes. Many deep and technically difficult results of the authors and his collaborators appear in the book. A must have for anyone interested in inference in diffusions." (Arup Bose, Sankhya: The Indian Journal of Statistics, Vol. 67 (1), 2005)
"This book is very much in the Springer mould of graduate mathematical statistics books, giving rapid access to the latest literature. ... It presents a strong discussion of nonparametric and semiparametric results, from both classical and Bayesian standpoints. The book will be of greatest use to mathematical statisticians, and as a reference work for those highly mathematical financial analysts who are involved in pricing, monitoring and trading derivatives. ... I have no doubt that it will come to be regarded as a classic text." (Mohamed Afzal Norat, Journal of the Royal Statistical Society, Vol. 167 (4), 2004)
"This work is a continuation of the study of large sample theory of continuous time stochastic processes investigated by the author ... . The book is written in a very clear style and is of use for research workers in the area of stochastic processes." (B. L. S. Prakasa Rao, Zentralblatt MATH, Vol. 1038 (13), 2004)

Product details

• Authors: Y. Kutoyants, Yu A. Kutoyants, Yury A Kutoyants, Yury a. Kutoyants
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 04.12.2003
• EAN: 9781852337599
• ISBN: 978-1-85233-759-9
• No. of pages: 482
• Dimensions: 156 mm x 245 mm x 29 mm
• Weight: 942 g
• Illustrations: XIV, 482 p.
• Series: Springer Series in Statistics; Springer Texts in Statistics; Springer Texts in Statistics; Springer Series in Statistics; Springer Statistics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics