Overview

This book collects and compares the results — mostly strong theorems which describe the properties of a simple symmetric random walk. The newest problems of limit theorems of probability theory are treated in the very simple case of coin tossing. Using the advantage of this simple situation, the reader can become familiar with limit theorems (especially strong ones) without suffering from technical tools and difficulties. A simple way to the study of the Wiener process is also given, through the study of the random walk. This book presents the most complete study of, and the most elementary way to the study of, the path properties of the Wiener process; and the most elementary way to the study of the strong theorems of probability theory.

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9789810202378

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Reviews

The expert will get as much out of the book as will the novice. It makes ideal reading material for a graduate course on the subject. As the Hungarian follow-up to Spitzer's classic, I am convinced that many will be grateful for the creation of this excellent monograph. Paul Embrechts Zurich, Switzerland The book will be useful to the many devotees of random walk and should attract more people to the area. H Kesten (1-CRNL) Mathematical Reviews, 1992 This useful and fascinating monograph gives a detailed description of the latest results on a broad spectrum of problems concerning the simple random walk {Sn} on the lattice Zd and their relation (invariance principle) to analogous problems for Brownian motion. Perhaps half of these results are proved in full detail. Many results appear here for the first time in book form. The book is very readable. J H B Kemperman SIAM Review, USA, 1992 A number of recent results and interesting open problems are presented, which have not appeared in any other book so far. The style of writing is clear and pleasant. The book is recommended for both introductory and advanced courses and also for researchers in probability theory and statistical physics. Endre Csaki Statistics & Decisions, 1993

""" The expert will get as much out of the book as will the novice. It makes ideal reading material for a graduate course on the subject. As the ""Hungarian"" follow-up to Spitzer's classic, I am convinced that many will be grateful for the creation of this excellent monograph."" Paul Embrechts Zurich, Switzerland ""The book will be useful to the many devotees of random walk and should attract more people to the area."" H Kesten (1-CRNL) Mathematical Reviews, 1992 ""This useful and fascinating monograph gives a detailed description of the latest results on a broad spectrum of problems concerning the simple random walk {Sn} on the lattice Zd and their relation (invariance principle) to analogous problems for Brownian motion. Perhaps half of these results are proved in full detail. Many results appear here for the first time in book form. The book is very readable."" J H B Kemperman SIAM Review, USA, 1992 ""A number of recent results and interesting open problems are presented, which have not appeared in any other book so far. The style of writing is clear and pleasant. The book is recommended for both introductory and advanced courses and also for researchers in probability theory and statistical physics."" Endre Csaki Statistics & Decisions, 1993"

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