دانلود کتاب Statistical Methods for Stochastic Differential Equations

"Preface The chapters of this volume represent the revised versions of the main papers given at the seventh Séminaire Européen de Statistique on "Statistics for Stochastic Differential Equations Models", held at La Manga del Mar Menor, Cartagena, Spain, May 7th-12th, 2007. The aim of the Sþeminaire Europþeen de Statistique is to provide talented young researchers with an opportunity to get quickly to the forefront of knowledge and research in areas of statistical science which are of major current interest. As a consequence, this volume is tutorial, following the tradition of the books based on the previous seminars in the series entitled: Networks and Chaos - Statistical and Probabilistic Aspects. Time Series Models in Econometrics, Finance and Other Fields. Stochastic Geometry: Likelihood and Computation. Complex Stochastic Systems. Extreme Values in Finance, Telecommunications and the Environment. Statistics of Spatio-temporal Systems. About 40 young scientists from 15 different nationalities mainly from European countries participated. More than half presented their recent work in short communications; an additional poster session was organized, all contributions being of high quality. The importance of stochastic differential equations as the modeling basis for phenomena ranging from finance to neurosciences has increased dramatically in recent years. Effective and well behaved statistical methods for these models are therefore of great interest. However the mathematical complexity of the involved objects raise theoretical but also computational challenges. The Séminaire and the present book present recent developments that address, on one hand, properties of the statistical structure of the corresponding models and,"-- Read more... Estimating functions for diffusion-type processes, Michael Sorensen Introduction Low frequency asymptotics Martingale estimating functions The likelihood function Non-martingale estimating functions High-frequency asymptotics High-frequency asymptotics in a fixed time-interval Small-diffusion asymptotics Non-Markovian models General asymptotic results for estimating functions Optimal estimating functions: General theory The econometrics of high frequency data, Per. A. Mykland and Lan Zhang Introduction Time varying drift and volatility Behavior of estimators: Variance Asymptotic normality Microstructure Methods based on contiguity Irregularly spaced data Statistics and high frequency data, Jean Jacod Introduction What can be estimated? Wiener plus compound Poisson processes Auxiliary limit theorems A first LNN (Law of Large Numbers) Some other LNNs A first CLT CLT with discontinuous limits Estimation of the integrated volatility Testing for jumps Testing for common jumps The Blumenthal-Getoor index Importance sampling techniques for estimation of diffusion models, Omiros Papaspiliopoulos and Gareth Roberts Overview of the chapter Background IS estimators based on bridge processes IS estimators based on guided processes Unbiased Monte Carlo for diffusions Appendix: Typical problems of the projection-simulation paradigm in MC for diffusions Appendix: Gaussian change of measure Non parametric estimation of the coefficients of ergodic diffusion processes based on high frequency data, Fabienne Comte, Valentine Genon-Catalot, and Yves Rozenholc Introduction Model and assumptions Observations and asymptotic framework Estimation method Drift estimation Diffusion coefficient estimation Examples and practical implementation Bibliographical remarks Appendix. Proof of Proposition.13 Ornstein-Uhlenbeck related models driven by Levy processes, Peter J. Brockwell and Alexander Lindner Introduction Levy processes Ornstein-Uhlenbeck related models Some estimation methods Parameter estimation for multiscale diffusions: an overview, Grigorios A. Pavliotis, Yvo Pokern, and Andrew M. Stuart Introduction Illustrative examples Averaging and homogenization Subsampling Hypoelliptic diffusions Nonparametric drift estimation Conclusions and further work