Weak Convergence and Its Applications

Publisher:

World Scientific

Publication Date:

2014

Number of Pages:

176

Format:

Hardcover

Price:

82.00

ISBN:

9789814447690

Category:

Monograph

We do not plan to review this book.

The Definition and Basic Properties of Weak Convergence:
- Metric Space
- The Definition of Weak Convergence of Stochastic Processes and Portmanteau Theorem
- How to Verify the Weak Convergence?
- Two Examples of Applications of Weak Convergence
Convergence to the Independent Increment Processes:
- The Basic Conditions of Convergence to the Gaussian Independent Increment Processes
- Donsker Invariance Principle
- Convergence of Poisson Point Processes
- Two Examples of Applications of Point Process Method
Convergence to Semimartingales:
- The Conditions of Tightness for Semimartingale Sequence
- Weak Convergence to Semimartingale
- Weak Convergence to Stochastic Integral I: The Martingale Convergence Approach
- Weak Convergence to Stochastic Integral II: Kurtz and Protter's Approach
- Stable Central Limit Theorem for Semimartingales
- An Application to Stochastic Differential Equations
- Appendix: The Predictable Characteristics of Semimartingales
Convergence of Empirical Processes:
- Classical Weak Convergence of Empirical Processes
- Weak Convergence of Marked Empirical Processes
- Weak Convergence of Function Index Empirical Processes
- Weak Convergence of Empirical Processes Involving Time-Dependent data
- Two Examples of Applications in Statistics