Like its predecessor, this book 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 theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
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Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
Les mer
Preface to the First Edition.- Preface to the Second Edition.- Outline of Contents.- Notation and Symbols.- Introductory Measure Theory.- Random Variables.- Inequalities.- Characteristic Functions.- Convergence.- The Law of Large Numbers.- The Central Limit Theorem.- The Law of the Iterated Logarithm.- Limited Theorems.- Martingales.- Some Useful Mathematics.- References.- Index.
Les mer
Like its predecessor, this book 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 theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
Les mer
From the reviews of the second edition:“This book of over 600 pages gives a self-contained presentation of modern probability theory. This is an updated edition of an elementary introductory book on probability theory … . Suitable as a textbook for beginning students in mathematics, statistics, computer science or economics … . Also, it will be very useful to students and researchers in mathematics or theoretical physics.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1267, 2013)
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Covers probability from a very applied perspective Many exercises involve mathematical modeling of random phenomena in very practical fields, including insurance/actuarial and the life sciences/biomedicine Second edition comprehensively updated, including all new exercises Includes supplementary material: sn.pub/extras
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Produktdetaljer
ISBN
9781489997555
Publisert
2014-11-09
Utgave
2. utgave
Utgiver
Vendor
Springer-Verlag New York Inc.
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Forfatter