Semimartingales and Their Statistical Inference

Cover
 Title Page
 Copyright Page
 Contents
 Preface
 1 Semimartingales
 1.1 Introduction
 1.2 Stochastic Processes
 Martingales
 1.3 Doob-Meyer Decomposition
 1.4 Stochastic Integration
 Stochastic Integrals with Respect to a Wiener Process
 Stochastic Integration with Respect to a Square Integrable Martingale
 Quadratic Characteristic and Quadratic Variation Processes
 Central Limit Theorem
 1.5 Local Martingales
 Stochastic Integral with Respect to a Local Martingale
 Some Inequalities for Local Martingales
 Strong Law of Large Numbers
 A Martingale Conditional Law Limit Theorems for Continuous Local MartingalesSome Additional Results on Stochastic Integrals with Respect to Square Integrable Local Martingales
 1.6 Semimartingales
 Stochastic Integral with Respect to a Semimartingale
 Product Formulae for Semimartingales
 Generalized Ito-Ventzell Formula
 Convergence of Quadratic Variation of Semimartingales
 Yoerup\'s Theorem for Local Martingales
 Stochastic Differential Equations
 Random Measures
 Stochastic Integral with Respect to the Measure µ --
v
 Decomposition of Local Martingales Using Stochastic Integrals
 1.7 Girsanov\'s Theorem Girsanov\'s Theorem for SemimartingalesGirsanov\'s Theorem for Semimartingales (Multidimensional Version)
 Gaussian Martingales
 1.8 Limit Theorems for Semimartingales
 Stable Convergence of Semimartingales
 1.9 Diffusion-Type Processes
 Diffusion Processes
 Eigen Functions and Martingales
 Stochastic Modeling
 Examples of Diffusion Processes
 Diffusion-Type Processes
 1.10 Point Processes
 Univariate Point Process (Simple)
 Multivariate Point Process
 Doubly Stochastic Poisson Process
 Stochastic Time Change
 References
 2 Exponential Families of Stochastic Processes
 2.1 Introduction 2.2 Exponential Families of Semimartingales2.3 Stochastic Time Transformation
 References
 3 Asymptotic Likelihood Theory
 3.1 Introduction
 Different Types of Information and Their Relationships
 3.2 Examples
 3.3 Asymptotic Likelihood Theory for a Class of Exponential Families of Semimartingales
 3.4 Asymptotic Likelihood Theory for General Processes
 3.5 Exercises
 References
 4 Asymptotic Likelihood Theory for Diffusion Processes with Jumps
 4.1 Introduction
 Diffusions with Jumps
 4.2 Absolute Continuity for Measures Generated by Diffusions with Jumps 4.3 Score Vector and Information Matrix4.4 Asymptotic Likelihood Theory for Diffusion Processes with Jumps
 Consistency
 Limiting Distribution
 4.5 Asymptotic Likelihood Theory for a Special Class of Exponential Families
 4.6 Examples
 4.7 Exercises
 References
 5 Quasi Likelihood and Semimartingales
 5.1 Quasi Likelihood and Discrete Time Processes
 5.2 Quasi Likelihood and Continuous Time Processes
 5.3 Quasi Likelihood and Special Sernimartingale
 Optimality
 Asymptotic Properties
 Existence and Consistency of the Quasi Likelihood Estimator