Statistical Methods for Stochastic Differential Equations

Statistical Methods for Stochastic Differential Equations

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Statistical Methods for Stochastic Differential Equations

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Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

17.05.2012

Verlag

Taylor & Francis

Seitenzahl

508

Beschreibung

Rezension

"... an excellent resource for anyone currently active in research in this area, interested in getting into research in the area, or just interested in the topic. I cannot think of another source that provides detailed yet accessible introductions of this quality and timeliness to the major issues of interest in this area. ... As noted in the preface, the idea is to get young researchers 'quickly to the forefront of knowledge and research.' ... The book succeeds in delivering on this goal. A careful reading of the chapters of this book would go a long way toward putting one in a position to begin contributing to the large and rapidly growing body of research in this important area of statistics. It would certainly be an excellent resource for teaching advanced Ph.D. courses. ... This is a wonderful book for anyone interested in SDEs. I highly recommend it and am happy to have it on my bookshelf."
-Garland B. Durham, Journal of the American Statistical Association, March 2014

"The contributors are all renowned specialists in the field ... the last four chapters are generally well written, informative, and cover a wide range of different aspects of statistics for SDE ... the first three chapters ... constitute an original and very useful contribution in a field that too often has the reputation of being technical and somehow austere. ... I strongly recommend the book for anyone interested in the wide topic of statistical methods for SDE, whether she or he is a specialist or a student starting in the field."
-Marc Hoffmann, Université Paris-Dauphine Sørensen, CHANCE, 26.3

"... a good collection of useful and interesting articles ... [I have] no hesitation in recommending the book."
-Tusheng Zhang, Journal of Time Series Analysis, 2013

Zitat

"... a good collection of useful and interesting articles ... [I have] no hesitation in recommending the book." -Tusheng Zhang, Journal of Time Series Analysis, 2013

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

17.05.2012

Verlag

Taylor & Francis

Seitenzahl

508

Maße (L/B/H)

23,4/15,5/3,3 cm

Gewicht

839 g

Sprache

Englisch

ISBN

978-1-4398-4940-8

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  • Statistical Methods for Stochastic Differential Equations
  • Estimating functions for diffusion-type processes, Michael SørensenIntroductionLow frequency asymptoticsMartingale estimating functionsThe likelihood functionNon-martingale estimating functionsHigh-frequency asymptoticsHigh-frequency asymptotics in a fixed time-intervalSmall-diffusion asymptoticsNon-Markovian modelsGeneral asymptotic results for estimating functionsOptimal estimating functions: General theoryThe econometrics of high frequency data, Per. A. Mykland and Lan ZhangIntroductionTime varying drift and volatilityBehavior of estimators: VarianceAsymptotic normalityMicrostructureMethods based on contiguityIrregularly spaced dataStatistics and high frequency data, Jean JacodIntroductionWhat can be estimated?Wiener plus compound Poisson processesAuxiliary limit theoremsA first LNN (Law of Large Numbers)Some other LNNsA first CLTCLT with discontinuous limitsEstimation of the integrated volatilityTesting for jumpsTesting for common jumpsThe Blumenthal–Getoor indexImportance sampling techniques for estimation of diffusion models, Omiros Papaspiliopoulos and Gareth RobertsOverview of the chapterBackgroundIS estimators based on bridge processesIS estimators based on guided processesUnbiased Monte Carlo for diffusionsAppendix: Typical problems of the projection-simulation paradigm in MC for diffusionsAppendix: Gaussian change of measureNon parametric estimation of the coefficients of ergodic diffusion processes based on high frequency data, Fabienne Comte, Valentine Genon-Catalot, and Yves RozenholcIntroductionModel and assumptionsObservations and asymptotic frameworkEstimation methodDrift estimationDiffusion coefficient estimationExamples and practical implementationBibliographical remarksAppendix. Proof of Proposition.13Ornstein–Uhlenbeck related models driven by Lévy processes, Peter J. Brockwell and Alexander LindnerIntroductionLévy processesOrnstein–Uhlenbeck related modelsSome estimation methodsParameter estimation for multiscale diffusions: an overview, Grigorios A. Pavliotis, Yvo Pokern, and Andrew M. StuartIntroductionIllustrative examplesAveraging and homogenizationSubsamplingHypoelliptic diffusionsNonparametric drift estimationConclusions and further work