Probability: A Graduate Course (Relié)

Like its predecessor, this hook starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability : the law of large numbers, the central limit theorem, and the law of the iterated logarithm.
Aber a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including scores of new problems and exercises, as well as new sections in the Inequalities and Random Variables chapters.