Martingale Limit Theory and Its Application (Probability and Mathematical Statistics)

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Dedication, Page iv Copyright, Page iv Preface, Pages ix-xi Notation, Page xii 1 - Introduction, Pages 1-11 2 - Inequalities and Laws of Large Numbers, Pages 13-50 3 - The Central Limit Theorem, Pages 51-96 4 - Invariance Principles in the Central Limit Theorem and Law of the Iterated Logarithm, Pages 97-125 5 - Limit Theory for Stationary Processes via Corresponding Results for Approximating Martingales, Pages 127-153 6 - Estimation of Parameters from Stochastic Processes, Pages 155-199 7 - Miscellaneous Applications, Pages 201-267 Appendix, Pages 269-283 References, Pages 285-297 Index to Theorems, Corollaries, and Examples, Pages 299-300 Index*, Pages 301-308 P. Hall And C. C. Heyde. Includes Indexes. Bibliography: P. 285-297.