Probability Theory : Independence, Interchangeability, Martingales. Yuan S. Chow , Henry Teicher. Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.
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Integration in a Probability Space. Sums of Independent Random Variables. Distribution Functions and Characteristic Functions.
Central Limit Theorems. Limit Theorems for Independent Random Variables. Infinitely Divisible Laws. Back Matter Pages About this book Introduction Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world.
Results as significant as the Bernoulli weak law of large numbers appeared as early as , although its counterpart, the Borel strong law oflarge numbers, did not emerge until Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes , von Mises ; , and Kolmogorov An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov.
The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome. Probability Probability theory Wahrscheinlichkeit Wahrscheinlichkeitsrechnung law of large numbers. Buy options.
It seems that you're in Germany. We have a dedicated site for Germany. Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated 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.
Probability Theory: Independence, Interchangeability, Martingales