Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

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Yes, you can access Martingale Limit Theory and Its Application by P. Hall,C. C. Heyde, Z. W. Birnbaum,E. Lukacs in PDF and/or ePUB format, as well as other popular books in Mathematik & Angewandte Mathematik. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Academic Press

Year

2014

ISBN

9781483263229

Topic

Mathematik

Subtopic

Angewandte Mathematik

Front Cover
Martingale Limit Theory and its Application
Copyright Page
Table of Contents
Preface
Notation
Chapter 1. Introduction
Chapter 2. Inequalities and Laws ofLarge Numbers
Chapter 3. The Central Limit Theorem
Chapter 4. Invariance Principles in the Central Limit Theorem and Law of the Iterated Logarithm
Chapter 5. Limit Theory for Stationary Processes via Corresponding Results for Approximating Martingales
Chapter 6. Estimation of Parameters from Stochastic Processes
Chapter 7. Miscellaneous Applications
Appendix
References
Index to T'heorem, and Examples
Index