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Large Deviations for Stochastic Processes
 
Jin Feng University of Kansas, Lawrence, KS
Thomas G. Kurtz University of Wisconsin at Madison, Madison, WI
Front Cover for Large Deviations for Stochastic Processes
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
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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
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  • Front Cover for Large Deviations for Stochastic Processes
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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.

    Readership

    Graduate students and research mathematicians interested in stochastic processes.

  • Table of Contents
     
     
    • 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
  • Request Review Copy
  • Get Permissions
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.

Readership

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
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