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Large Deviations for Stochastic Processes
About this Title
Jin Feng, University of Kansas, Lawrence, KS and Thomas G. Kurtz, University of Wisconsin at Madison, Madison, WI
Publication: Mathematical Surveys and Monographs
Publication Year:
2006; Volume 131
ISBNs: 978-1-4704-1870-0 (print); 978-1-4704-1358-3 (online)
DOI: https://doi.org/10.1090/surv/131
MathSciNet review: MR2260560
MSC: Primary 60F10; Secondary 60-02, 60J05, 60J25
Table of Contents
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Front/Back Matter
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