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
- The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof
- Development and applications of the second moment analogue of Walds equation
- Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem
- Complete discussion, including central limit theorem, of the random casting of r balls into n cells
- Recent martingale inequalities
- Cram r-L vy theorem and factor-closed families of distributions.
- ISBN13 9780387982281
- Publish Date 11 September 1997 (first published 19 December 1978)
- Publish Status Active
- Publish Country US
- Imprint Springer-Verlag New York Inc.
- Edition 3rd ed. 1997
- Format Hardcover
- Pages 489
- Language English