Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications
 
Ph. Barbe CNRS, Paris, France
W. P. McCormick University of Georgia, Athens
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications
eBook ISBN:  978-1-4704-0528-1
Product Code:  MEMO/197/922.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications
Click above image for expanded view
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications
Ph. Barbe CNRS, Paris, France
W. P. McCormick University of Georgia, Athens
eBook ISBN:  978-1-4704-0528-1
Product Code:  MEMO/197/922.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1972009; 117 pp
    MSC: Primary 41; 60; Secondary 44; 62;

    The authors establish some asymptotic expansions for infinite weighted convolution of distributions having regularly varying tails. Applications to linear time series models, tail index estimation, compound sums, queueing theory, branching processes, infinitely divisible distributions and implicit transient renewal equations are given.

    A noteworthy feature of the approach taken in this paper is that through the introduction of objects, which the authors call the Laplace characters, a link is established between tail area expansions and algebra. By virtue of this representation approach, a unified method to establish expansions across a variety of problems is presented and, moreover, the method can be easily programmed so that a computer algebra package makes implementation of the method not only feasible but simple.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Main result
    • 3. Implementing the expansion
    • 4. Applications
    • 5. Preparing the proof
    • 6. Proof in the positive case
    • 7. Removing the sign restriction on the random variables
    • 8. Removing the sign restriction on the constants
    • 9. Removing the smoothness restriction
    • Appendix. Maple code
  • 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: 1972009; 117 pp
MSC: Primary 41; 60; Secondary 44; 62;

The authors establish some asymptotic expansions for infinite weighted convolution of distributions having regularly varying tails. Applications to linear time series models, tail index estimation, compound sums, queueing theory, branching processes, infinitely divisible distributions and implicit transient renewal equations are given.

A noteworthy feature of the approach taken in this paper is that through the introduction of objects, which the authors call the Laplace characters, a link is established between tail area expansions and algebra. By virtue of this representation approach, a unified method to establish expansions across a variety of problems is presented and, moreover, the method can be easily programmed so that a computer algebra package makes implementation of the method not only feasible but simple.

  • Chapters
  • 1. Introduction
  • 2. Main result
  • 3. Implementing the expansion
  • 4. Applications
  • 5. Preparing the proof
  • 6. Proof in the positive case
  • 7. Removing the sign restriction on the random variables
  • 8. Removing the sign restriction on the constants
  • 9. Removing the smoothness restriction
  • Appendix. Maple code
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.