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Large Deviations for Stochastic Processes

Jin Feng University of Kansas, Lawrence, KS
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Softcover ISBN: 978-1-4704-1870-0
Product Code: SURV/131.S
List Price: $102.00 MAA Member Price:$91.80
AMS Member Price: $81.60 Electronic ISBN: 978-1-4704-1358-3 Product Code: SURV/131.E List Price:$102.00
MAA Member Price: $91.80 AMS Member Price:$81.60
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List Price: $153.00 MAA Member Price:$137.70
AMS Member Price: $122.40 Click above image for expanded view Large Deviations for Stochastic Processes Jin Feng University of Kansas, Lawrence, KS Thomas G. Kurtz University of Wisconsin at Madison, Madison, WI Available Formats:  Softcover ISBN: 978-1-4704-1870-0 Product Code: SURV/131.S  List Price:$102.00 MAA Member Price: $91.80 AMS Member Price:$81.60
 Electronic ISBN: 978-1-4704-1358-3 Product Code: SURV/131.E
 List Price: $102.00 MAA Member Price:$91.80 AMS Member Price: $81.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$153.00 MAA Member Price: $137.70 AMS Member Price:$122.40
• Book Details

Mathematical Surveys and Monographs
Volume: 1312006; 410 pp
MSC: Primary 60; 47; Secondary 49;

The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.

Graduate students and research mathematicians interested in stochastic processes.

• Chapters
• 1. Introduction
• 2. An overview
• 3. Large deviations and exponential tightness
• 4. Large deviations for stochastic processes
• 5. Large deviations for Markov processes and nonlinear semigroup convergence
• 6. Large deviations and nonlinear semigroup convergence using viscosity solutions
• 7. Extensions of viscosity solution methods
• 8. The Nisio semigroup and a control representation of the rate function
• 9. The comparison principle
• 10. Nearly deterministic processes in $R^d$
• 11. Random evolutions
• 12. Occupation measures
• 13. Stochastic equations in infinite dimensions
• Appendix A. Operators and convergence in function spaces
• Appendix B. Variational constants, rate of growth and spectral theory for the semigroup of positive linear operators
• Appendix C. Spectral properties for discrete and continuous Laplacians
• Appendix D. Results from mass transport theory

• Reviews

• This book is an excellent introduction to the art of large deviations for Markov processes.

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1312006; 410 pp
MSC: Primary 60; 47; Secondary 49;

The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.

Graduate students and research mathematicians interested in stochastic processes.

• Chapters
• 1. Introduction
• 2. An overview
• 3. Large deviations and exponential tightness
• 4. Large deviations for stochastic processes
• 5. Large deviations for Markov processes and nonlinear semigroup convergence
• 6. Large deviations and nonlinear semigroup convergence using viscosity solutions
• 7. Extensions of viscosity solution methods
• 8. The Nisio semigroup and a control representation of the rate function
• 9. The comparison principle
• 10. Nearly deterministic processes in $R^d$
• 11. Random evolutions
• 12. Occupation measures
• 13. Stochastic equations in infinite dimensions
• Appendix A. Operators and convergence in function spaces
• Appendix B. Variational constants, rate of growth and spectral theory for the semigroup of positive linear operators
• Appendix C. Spectral properties for discrete and continuous Laplacians
• Appendix D. Results from mass transport theory
• This book is an excellent introduction to the art of large deviations for Markov processes.

Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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