همگرایی تصادفی (احتمال و آمار ریاضی؛ جلد ۳۰)

Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students. Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems.This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes.This book will prove useful to mathematicians and advanced mathematics students. Content: Front Matter, Page iii Copyright, Page iv PREFACE TO THE SECOND EDITION, Page vii PREFACE TO THE FIRST EDITION, Pages ix-x LIST OF EXAMPLES†, Page xi CHAPTER I - INTRODUCTION, Pages 1-26 CHAPTER II - STOCHASTIC CONVERGENCE CONCEPTS AND THEIR PROPERTIES, Pages 27-59 CHAPTER III - SPACES OF RANDOM VARIABLES, Pages 60-75 CHAPTER IV - INFINITE SERIES OF RANDOM VARIABLES AND RELATED TOPICS, Pages 76-111 CHAPTER V - RANDOM POWER SERIES, Pages 112-142 CHAPTER VI - STOCHASTIC INTEGRALS AND DERIVATIVES, Pages 143-156 CHAPTER VII - CHARACTERIZATION OF THE NORMAL DISTRIBUTION BY PROPERTIES OF INFINITE SUMS OF RANDOM VARIABLES, Pages 157-171 CHAPTER VIII - CHARACTERIZATION OF SOME STOCHASTIC PROCESSES, Pages 172-190 REFERENCES, Pages 191-194 Index, Pages 195-200 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2 Eugene Lukacs. Includes Index. Bibliography: P. [191]-194.