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Simulation and inference for stochastic differential equations. With R examples. (English) Zbl 1210.62112
Springer Series in Statistics. New York, NY: Springer (ISBN 978-0-387-75838-1/hbk). xviii, 284 p. (2008).
Diffusion processes, described by stochastic differential equations (SDEs), are extensively applied in many areas of scientific research. This book focuses on simulation techniques and parameter estimation for SDEs. It gives an overview of these topics through a mix of simplified theory and examples. The book is written in a way to be suitable for the beginner and the advanced reader who want to know about new directions in numerics or inference.
The book starts with the basic theory of stochastic processes and SDEs. Some introductory material on simulation is also included. Numerical methods for SDEs are discussed next. The chapter on parameter estimation introduces some novel techniques for inference. There is also a small chapter on miscellaneous topics which contains the Akaike information criterion, nonparametric estimation and change-point estimation. Essentially all examples are complemented by program codes in R. The appendix presents a brief excursion into R and a description of the R-functions that are used throughout the book.

MSC:
62M05 Markov processes: estimation; hidden Markov models
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C60 Computational problems in statistics (MSC2010)
65C50 Other computational problems in probability (MSC2010)
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M99 Inference from stochastic processes
Software:
R; ISwR; S-PLUS; sde
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