Bernstein Functions: Theory and Applications

Hardcover (Print)
Buy New
Buy New from BN.com
$119.70
Used and New from Other Sellers
Used and New from Other Sellers
from $95.50
Usually ships in 1-2 business days
(Save 24%)
Other sellers (Hardcover)
  • All (3) from $95.50   
  • New (2) from $95.50   
  • Used (1) from $113.57   

Overview

This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided.
Read More Show Less

Product Details

Meet the Author

René Schilling, Dresden University of Technology, Germany; Renming Song, University of Illinois, Urbana, USA; Zoran Vondracek, University of Zagreb, Croatia.
Read More Show Less

Table of Contents

Preface vii

Index of notation xii

1 Completely monotone functions 1

2 Stieltjes functions 11

3 Bernstein functions 15

4 Positive and negative definite functions 25

5 A probabilistic intermezzo 34

6 Complete Bernstein functions: representation 49

7 Complete Bernstein functions: properties 62

8 Thorin-Bernstein functions 73

9 A second probabilistic intermezzo 80

10 Special Bernstein functions and potentials 92

10.1 Special Bernstein functions 92

10.2 Hirsch's class 105

11 The spectral theorem and operator monotonicity 110

11.1 The spectral theorem 110

11.2 Operator monotone functions 118

12 Subordination and Bochner's functional calculus 130

12.1 Semigroups and subordination in the sense of Bochner 130

12.2 A functional calculus for generators of semigroups 145

12.3 Eigenvalue estimates for subordinate processes 161

13 Potential theory of subordinate killed Brownian motion 174

14 Applications to generalized diffusions 185

14.1 Inverse local time at zero 185

14.2 First passage times 202

15 Examples of complete Bernstein functions 214

15.1 Special functions used in the tables 215

15.2 Algebraic functions 218

15.3 Exponential functions 226

15.4 Logarithmic functions 228

15.5 Inverse trigonometric functions 244

15.6 Hyperbolic functions 244

15.7 Inverse hyperbolic functions 250

15.8 Gamma and other special functions 254

15.9 Bessel functions 264

15.10 Miscellaneous functions 272

15.11 Additional comments 278

A Appendix 281

A.1 Vague and weak convergence of measures 281

A.2 Hunt processes and Dirichlet forms 283

Bibliography 291

Index 309

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)