A Weak Convergence Approach to the Theory of Large Deviations / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$170.33
Used and New from Other Sellers
Used and New from Other Sellers
from $123.00
Usually ships in 1-2 business days
(Save 41%)
Other sellers (Hardcover)
  • All (8) from $123.00   
  • New (4) from $171.71   
  • Used (4) from $123.00   

Overview

Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis—a consistent new approach

The theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty. This innovative text demonstrates how to employ the well-established linear techniques of weak convergence theory to prove large deviation results. Beginning with a step-by-step development of the approach, the book skillfully guides readers through models of increasing complexity covering a wide variety of random variable-level and process-level problems. Representation formulas for large deviation-type expectations are a key tool and are developed systematically for discrete-time problems.

Accessible to anyone who has a knowledge of measure theory and measure-theoretic probability, A Weak Convergence Approach to the Theory of Large Deviations is important reading for both students and researchers.

Read More Show Less

Editorial Reviews

Booknews
Applies the well established linear techniques of weak convergence theory to the nonlinear theory of large derivations, thus overcoming some of its difficulties while continuing to exploit its richness in investigating rare events in stochastic systems. Develops the approach step by step through increasing complexity covering a wide range of problems at the both the variable and the process levels. Assumes a knowledge of measure theory and measure-theoretic probability. Annotation c. by Book News, Inc., Portland, Or.
Read More Show Less

Product Details

Meet the Author

PAUL DUPUIS is a professor in the Division of Applied Mathematics at Brown University in Providence, Rhode Island.

RICHARD S. ELLIS is a professor in the Department of Mathematics and Statistics at the University of Massachusetts at Amherst.

Read More Show Less

Table of Contents

Formulation of Large Deviation Theory in Terms of the Laplace Principle.

First Example: Sanov's Theorem.

Second Example: Mogulskii's Theorem.

Representation Formulas for Other Stochastic Processes.

Compactness and Limit Properties for the Random Walk Model.

Laplace Principle for the Random Walk Model with Continuous Statistics.

Laplace Principle for the Random Walk Model with Discontinuous Statistics.

Laplace Principle for the Empirical Measures of a Markov Chain.

Extensions of the Laplace Principle for the Empirical Measures of a Markov Chain.

Laplace Principle for Continuous-Time Markov Processes with Continuous Statistics.

Appendices.

Bibliography.

Indexes.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)