Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. 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. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.
Continuous Sampling.- Parametric Stochastic 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 Stochastic 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.
From the reviews:
"This book deals with a variety of statistical inference problems for stochastic 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 stochastic modelling; especially those working in areas such as physics, engineering, biology and finance." (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1134 (12), 2008)
