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Moderate Deviations for the Range of Planar Random Walks
Available Formats:
Electronic ISBN: 9781470405359
Product Code: MEMO/198/929.E
List Price: $66.00
MAA Member Price: $59.40
AMS Member Price: $39.60
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Moderate Deviations for the Range of Planar Random Walks
Available Formats:
Electronic ISBN:  9781470405359 
Product Code:  MEMO/198/929.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $39.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 198; 2009; 82 ppMSC: Primary 60;
Given a symmetric random walk in \({\mathbb Z}^2\) with finite second moments, let \(R_n\) be the range of the random walk up to time \(n\). The authors study moderate deviations for \(R_n {\mathbb E}R_n\) and \({\mathbb E}R_n R_n\). They also derive the corresponding laws of the iterated logarithm.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. History

Chapter 3. Overview

Chapter 4. Preliminaries

Chapter 5. Moments of the range

Chapter 6. Moderate deviations for $R_n  \mathbb {E}R_n$

Chapter 7. Moderate deviations for $\mathbb {E}R_n  R_n$

Chapter 8. Exponential asymptotics for the smoothed range

Chapter 9. Exponential approximation

Chapter 10. Laws of the iterated logarithm


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 Book Details
 Table of Contents
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Volume: 198; 2009; 82 pp
MSC: Primary 60;
Given a symmetric random walk in \({\mathbb Z}^2\) with finite second moments, let \(R_n\) be the range of the random walk up to time \(n\). The authors study moderate deviations for \(R_n {\mathbb E}R_n\) and \({\mathbb E}R_n R_n\). They also derive the corresponding laws of the iterated logarithm.

Chapters

Chapter 1. Introduction

Chapter 2. History

Chapter 3. Overview

Chapter 4. Preliminaries

Chapter 5. Moments of the range

Chapter 6. Moderate deviations for $R_n  \mathbb {E}R_n$

Chapter 7. Moderate deviations for $\mathbb {E}R_n  R_n$

Chapter 8. Exponential asymptotics for the smoothed range

Chapter 9. Exponential approximation

Chapter 10. Laws of the iterated logarithm
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