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Moderate Deviations for the Range of Planar Random Walks

Richard F. Bass University of Connecticut, Storrs, CT
Xia Chen University of Tennessee, Knoxville, TN
Jay Rosen CUNY, College of Staten Island, Staten Island, NY
Available Formats:
Electronic ISBN: 978-1-4704-0535-9
Product Code: MEMO/198/929.E
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $39.60 Click above image for expanded view Moderate Deviations for the Range of Planar Random Walks Richard F. Bass University of Connecticut, Storrs, CT Xia Chen University of Tennessee, Knoxville, TN Jay Rosen CUNY, College of Staten Island, Staten Island, NY Available Formats:  Electronic ISBN: 978-1-4704-0535-9 Product Code: MEMO/198/929.E  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$39.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1982009; 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1982009; 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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