RANDOM WALK RANDOM & NON-RAND 3ED - Hardcover

PAL REVESZ

Hardcover

ISBN 10: 9814447501 ISBN 13: 9789814447508

Verlag: World Scientific, 2013

Inhaltsangabe

THE SIMPLEST MATHEMATICAL MODEL OF THE BROWNIAN MOTION OF PHYSICS IS THE SIMPLE, SYMMETRIC RANDOM WALK. THIS BOOK COLLECTS AND COMPARES CURRENT RESULTS - MOSTLY STRONG THEOREMS WHICH DESCRIBE THE PROPERTIES OF A RANDOM WALK. THE MODERN PROBLEMS OF THE LIMIT THEOREMS OF PROBABILITY THEORY ARE TREATED IN THE SIMPLE CASE OF COIN TOSSING. TAKING ADVANTAGE OF THIS SIMPLICITY, THE READER IS FAMILIARIZED WITH LIMIT THEOREMS (ESPECIALLY STRONG ONES) WITHOUT THE BURDEN OF TECHNICAL TOOLS AND DIFFICULTIES. AN EASY WAY OF CONSIDERING THE WIENER PROCESS IS ALSO GIVEN, THROUGH THE STUDY OF THE RANDOM WALK.SINCE THE FIRST AND SECOND EDITIONS WERE PUBLISHED IN 199 AND 25, A NUMBER OF NEW RESULTS HAVE APPEARED IN THE LITERATURE. THE FIRST TWO EDITIONS CONTAINED MANY UNSOLVED PROBLEMS AND CONJECTURES WHICH HAVE SINCE BEEN SETTLED; THIS THIRD, REVISED AND ENLARGED EDITION INCLUDES THOSE NEW RESULTS. IN THIS EDITION, A COMPLETELY NEW PART IS INCLUDED CONCERNING SIMPLE RANDOM WALKS ON GRAPHS. PROPERTIES OF RANDOM WALKS ON SEVERAL CONCRETE GRAPHS HAVE BEEN STUDIED IN THE LAST DECADE. SOME OF THE OBTAINED RESULTS ARE ALSO PRESENTED.

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Reseña del editor

The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results - mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.

Details zur Ausgabe

• Verlag: World Scientific
• Erscheinungsdatum: 2013
• ISBN 10: 9814447501
• ISBN 13: 9789814447508
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 3
• Anzahl der Seiten: 422