This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation.

Probability Theory (Courant Lecture Notes)

Science & Math

Varadhan, S.R.S.

Mathematics

Amer Mathematical Society

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.

Large Deviations and Applications (CBMS-NSF Regional Conference Series in Applied Mathematics, No. 46)

Society for Industrial & Applied Mathematics

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

Multidimensional Diffusion Processes (Classics in Mathematics)

Stroock, Daniel W.

Chemistry

Springer

"This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. (...) The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. (...) The reader must be familiar with standard probability theory and measure theory which are summarized at the beginning of the book. 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, 1981

Multidimensional Diffusion Processes (Grundlehren der mathematischen Wissenschaften)

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. Volume I includes the introductory material, the papers on limit theorems and review articles.

Collected Papers I: Limit Theorems

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 a 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 areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians.&nbsp;Varadhan was awarded the Abel Prize in 2007.&nbsp;These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.&nbsp; Volume II includes the papers on PDE, SDE, diffusions, and random media.&#8203;&#8203;

Collected Papers II: PDE, SDE, Diffusions, Random Media (Collecrted Papers II)

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. Volume IV includes the papers on particle systems.

Collected Papers IV: Particle Systems and Their Large Deviations (Collected Papers of S.r.s. Varadhan, 4)

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

Stroock, Daniel W. W.

See the best price to sell, buy, or rent books by Varadhan, S.R.S.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Varadhan, S.R.S.

See the best price to sell, buy, or rent books by Varadhan, S.R.S.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Probability Theory (Courant Lecture Notes)

Large Deviations and Applications (CBMS-NSF Regional Conference Series in Applied Mathematics, No. 46)

Multidimensional Diffusion Processes (Classics in Mathematics)

Multidimensional Diffusion Processes (Grundlehren der mathematischen Wissenschaften)

Collected Papers I: Limit Theorems

Collected Papers II: PDE, SDE, Diffusions, Random Media (Collecrted Papers II)

Collected Papers IV: Particle Systems and Their Large Deviations (Collected Papers of S.r.s. Varadhan, 4)

Multidimensional Diffusion Processes (Classics in Mathematics)