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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
Moderate Deviations for the Range of Planar Random Walks
eBook 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
Moderate Deviations for the Range of Planar Random Walks
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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
eBook 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.

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.