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.

“The book is very well organized and the structure of each chapter is helpful: notation, assumptions, statements, examples, proofs and comments are clearly separated. … this makes the book a good reference for researchers interested in rare event analysis and approximation.” (‪Charles-Edouard Bréhier, Mathematical Reviews, August, 2020)“The current book requires a solid background in weak convergence of probability measures and stochastic analysis, and it is intended for advanced graduate students, post-doctoral fellows and researchers working in this area.” (Anatoliy Swishchuk, zbMATH 1427.60003, 2020)

• Preliminaries and elementary examples.- Discrete time processes.- Continuous time processes.- Monte Carlo approximation.​

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.

“The book is very well organized and the structure of each chapter is helpful: notation, assumptions, statements, examples, proofs and comments are clearly separated. … this makes the book a good reference for researchers interested in rare event analysis and approximation.” (‪Charles-Edouard Bréhier, Mathematical Reviews, August, 2020)“The current book requires a solid background in weak convergence of probability measures and stochastic analysis, and it is intended for advanced graduate students, post-doctoral fellows and researchers working in this area.” (Anatoliy Swishchuk, zbMATH 1427.60003, 2020)

• Preliminaries and elementary examples.- Discrete time processes.- Continuous time processes.- Monte Carlo approximation.​