PROBABILITY THEORY IBD

Sinopse

Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: - A comprehensive treatment of the law of the iterated logarithm -áThe Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof -áDevelopment and applications of the second moment analogue of Walds equation -áLimit theorems for martingale arrays, the central limit theorem for the interchangeable and martingale cases, moment convergence in the central limit theorem -áComplete discussion, including central limit theorem, of the random casting of r balls into n cells -áRecent martingale inequalities -áCram r-L vy theorem and factor-closed families of distributions.