Parameter Estimation in Stochastic Differential Equations

2008
ISBN: 978-3-540-74447-4
Verlag: Springer-Verlag GmbH

Buch, Englisch, Band 1923, 268 Seiten, Book, Format (B × H): 157 mm x 237 mm, Gewicht: 452 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bishwal, Jaya P. N.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie

Inhaltsverzeichnis

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.