Description
Book SynopsisThe 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 edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion.
Trade Review"This book tells a very personal and exciting story from the point of view of one of the dominant contributors to the study of random walks, and will be of interest to those looking for intriguing open problems in the theory of random walks and associated strong limit laws." Mathematical Reviews "The reader interested in the theory of random walks in non-random environments and also on the associated strong limit laws will find this book very interesting and also very useful." Zentralblatt MATH
