Semimartingales and Their Statistical Inference

✍ Scribed by Rao, B. L. S. Prakasa

• Publisher: Routledge
• Year: 2018
• Tongue: English
• Leaves: 599
• Series: Chapman and Hall/CRC Monographs on Statistics and Applied Probability.
• Category: Library

✦ Table of Contents

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

✦ Subjects

Mathematical statistics -- Asymptotic theory;Semimartingales;Statistiek;Martingalen;Asymptotische analyse;Inferenzstatistik;Semimartingal;MATHEMATICS / Applied;MATHEMATICS / Probability & Statistics / General