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Probability Theory and Stochastic Modelling
cover

Analysis and Approximation of Rare Events

Representations and Weak Convergence Methods

Authors: Budhiraja, Amarjit, Dupuis, Paul

  • Illustrates  the use of these methods using a wide variety of discrete and continuous time models
  • Timely and important topic with significant developments over the last 15 years
  • Includes both theory and links with applications
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eBook $109.00
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • Due: September 23, 2019
  • ISBN 978-1-4939-9579-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $139.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: September 23, 2019
  • ISBN 978-1-4939-9577-6
  • Free shipping for individuals worldwide
About this book

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values.  By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation.  The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.


About the authors

Amarjit Budhiraja is a Professor of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He is a Fellow of the IMS. His research interests include stochastic analysis, the theory of large deviations, stochastic networks and stochastic nonlinear filtering.​
Paul Dupuis is the IBM Professor of Applied Mathematics at Brown University and a Fellow of the AMS, SIAM and IMS.  His research interests include stochastic control, the theory of large deviations and numerical methods.

Buy this book

eBook $109.00
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • Due: September 23, 2019
  • ISBN 978-1-4939-9579-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $139.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: September 23, 2019
  • ISBN 978-1-4939-9577-6
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Analysis and Approximation of Rare Events
Book Subtitle
Representations and Weak Convergence Methods
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
94
Copyright
2019
Publisher
Springer US
Copyright Holder
Springer Science+Business Media, LLC, part of Springer Nature
eBook ISBN
978-1-4939-9579-0
DOI
10.1007/978-1-4939-9579-0
Hardcover ISBN
978-1-4939-9577-6
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XIX, 582
Number of Illustrations
13 b/w illustrations, 1 illustrations in colour
Topics