Parameter estimation in stochastic differential equations

Jaya P. N. Bishwal (auth.)3540744479, 978-3-540-74447-4

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.

Table of contents :
Front Matter….Pages I-XII
Front Matter….Pages 13-13
Parametric Stochastic Differential Equations….Pages 1-11
Rates of Weak Convergence of Estimators in Homogeneous Diffusions….Pages 15-48
Large Deviations of Estimators in Homogeneous Diffusions….Pages 49-60
Local Asymptotic Mixed Normality for Nonhomogeneous Diffusions….Pages 61-78
Bayes and Sequential Estimation in Stochastic PDEs….Pages 79-97
Maximum Likelihood Estimation in Fractional Diffusions….Pages 99-122
Front Matter….Pages 123-123
Approximate Maximum Likelihood Estimation in Nonhomogeneous Diffusions….Pages 125-157
Rates of Weak Convergence of Estimators in the Ornstein-Uhlenbeck Process….Pages 159-200
Local Asymptotic Normality for Discretely Observed Homogeneous Diffusions….Pages 201-223
Estimating Function for Discretely Observed Homogeneous Diffusions….Pages 225-244
Back Matter….Pages 245-264