Memoirs of the American Mathematical Society
2009;
82 pp;
Softcover
MSC: Primary 60;
Print ISBN: 978-0-8218-4287-4
Product Code: MEMO/198/929
List Price: $66.00
AMS Member Price: $39.60
MAA Member Price: $59.40
Electronic ISBN: 978-1-4704-0535-9
Product Code: MEMO/198/929.E
List Price: $66.00
AMS Member Price: $39.60
MAA Member Price: $59.40
Moderate Deviations for the Range of Planar Random Walks
Share this pageRichard F. Bass; Xia Chen; Jay Rosen
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
Table of Contents
Moderate Deviations for the Range of Planar Random Walks
- Contents v6 free
- Abstract vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. History 514 free
- Chapter 3. Overview 918
- Chapter 4. Preliminaries 1322
- Chapter 5. Moments of the range 2130
- Chapter 6. Moderate deviations for R[sub(n)] – ER[sub(n)] 3342
- Chapter 7. Moderate deviations for ER[sub(n)] – R[sub(n)] 4150
- Chapter 8. Exponential asymptotics for the smoothed range 5362
- Chapter 9. Exponential approximation 6574
- Chapter 10. Laws of the iterated logarithm 7382
- Bibliography 8190