Background
Varadhan, Srinivasa S. R. was born on January 2, 1940 in Madras, India. Son of Ranga and Janaki Ayyangar. came to the United States, 1963.
(Many situations exist in which solutions to problems are ...)
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
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(Includes: Azencott, R: Large deviations and applications;...)
Includes: Azencott, R: Large deviations and applications; Freidlin, Mark I Semi-linear PDE's and limit theorems for large deviations; Varadhan, Srinivasa R S: Large deviations and applications.
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( Volume I includes the introductory material, the papers...)
Volume I includes the introductory material, the papers on limit theorems and review articles. Volume II features Varadhan's papers on PDE, SDE, diffusions, and random media. Volume III covers the papers on large deviations. Volume IV collects the papers on particle systems. From the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and of a young graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other topics in probability, analysis and physics, and collaborated with several distinguished mathematicians. These Collected Works contain all his research papers over the half-century from 1962 to early 2012.
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( From the reviews: "This book is an excellent presentati...)
From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. ... This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik
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(The theory of large deviations deals with rates at which ...)
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
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Varadhan, Srinivasa S. R. was born on January 2, 1940 in Madras, India. Son of Ranga and Janaki Ayyangar. came to the United States, 1963.
Bachelor of Science with honors, Madras U., India, 1959; Master of Arts, Madras U., India, 1959; Doctor of Philosophy, Indian Statistical Institute, Calcutta, 1963.
Instructor, Indian Statistical Institute, Calcutta, 1962-1963; visiting member, Courant Institute Mathematics Sciences, New York City, 1963-1966; assistant professor mathematics, Courant Institute Mathematics Sciences, New York City, 1966-1968; associate professor mathematics, Courant Institute Mathematics Sciences, New York City, 1968-1972; professor mathematics, Courant Institute Mathematics Sciences, New York City, since 1972; director, Courant Institute Mathematics Sciences, New York City, 1980-1984, 92-94.
(Includes: Azencott, R: Large deviations and applications;...)
( From the reviews: "This book is an excellent presentati...)
(The theory of large deviations deals with rates at which ...)
(Many situations exist in which solutions to problems are ...)
( Volume I includes the introductory material, the papers...)
Fellow Royal Society. Member NAS, American Academy Arts and Sciences, American Mathematics Society(George David Birkhoff Prize in applied mathematics 1994, Steele prize 1996), Society Industrial and Applied Mathematics, Institute Mathematics Sciences, Third World Academy Sciences.
Married Vasundara Narayanan, June 5, 1964. Children— Gopalakrishnan, Ashok.