Parameter Estimation in Stochastic Differential Equations

Overview

Parameter estimation in shastic differential equations and shastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

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Paperback (2008)
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Overview

Parameter estimation in shastic differential equations and shastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

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Editorial Reviews

From the Publisher
From the reviews:

"This book deals with a variety of statistical inference problems for shastic differential equations … . In each chapter the author starts with useful introductory notes clearly describing the specific models and the problems. … A series of interesting and well commented examples are provided as an illustration. … Among the readers who can benefit from this carefully written book are researchers and postgraduate students in shastic modelling; especially those working in areas such as physics, engineering, biology and finance." (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1134 (12), 2008)

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Product Details

  • ISBN-13: 9783540744474
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/9/2007
  • Series: Lecture Notes in Mathematics Series , #1923
  • Edition description: 2008
  • Edition number: 1
  • Pages: 268
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.70 (d)

Table of Contents

Continuous Sampling.- Parametric Shastic Differential Equations.- Rates of Weak Convergence of Estimators in Homogeneous Diffusions.- Large Deviations of Estimators in Homogeneous Diffusions.- Local Asymptotic Mixed Normality for Nonhomogeneous Diffusions.- Bayes and Sequential Estimation in Shastic PDEs.- Maximum Likelihood Estimation in Fractional Diffusions.- Discrete Sampling.- Approximate Maximum Likelihood Estimation in Nonhomogeneous Diffusions.- Rates of Weak Convergence of Estimators in the Ornstein-Uhlenbeck Process.- Local Asymptotic Normality for Discretely Observed Homogeneous Diffusions.- Estimating Function for Discretely Observed Homogeneous Diffusions.

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