Statistical Inference for Ergodic Diffusion Processes (Springer Series in Statistics)

**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__ 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

The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.

Front Matter....Pages i-xiii Introduction....Pages 1-16 Diffusion Processes and Statistical Problems....Pages 17-110 Parameter Estimation....Pages 111-226 Special Models....Pages 227-307 Nonparametric Estimation....Pages 309-419 Hypotheses Testing....Pages 421-460 Back Matter....Pages 461-482