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 reputationas 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. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.
Volume II includes the papers on PDE, SDE, diffusions, and random media.
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ISBN-13
978-3-642-33545-7 (9783642335457)
Schweitzer Klassifikation
Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi, India. He is the author of five books including "Matrix Analysis" and "Positive Definite Matrices".
Vol. II: Diffusion processes with continuous coefficients - I (with D. W. Stroock).- Diffusion processes with continuous coefficients - II (with D. W. Stroock).- Diffusion processes with boundary conditions (with D. W. Stroock).- On degenerate elliptic-parabolic operators of second order and their associated diffusions (with D. W. Stroock).- On the support of diffusion processes with applications to the strong maximum principle (with D. W. Stroock).- Diffusion processes (with D. W. Stroock).- A probabilistic approach to Hp(Rd) (with D. W. Stroock).- Kac functional and Schrodinger equation (with K. L. Chung).- Brownian motion in a wedge with oblique reection (with R. J. Williams).- A multidimensional process involving local time (with A.S. Sznitman).- Etat fondamental et principe du maximum pour les operateurs elliptiques du second ordre dans des domaines generaux. [The ground state and maximum principle for second-order elliptic operators in general domains] (with H. Berestycki and L.Nirenberg).- The principal eigenvalue and maximum principle for second-order elliptic operators in general domains (with H. Berestycki and L. Nirenberg).- Diffusion semigroups and di_usion processes corresponding to degenerate divergence form operators (with J. Quastel).- Random Media.- Diffusion in regions with many small holes (with G. Papanicolaou).- Boundary value problems with rapidly oscillating random coefficients (with G. Papanicolaou).- Diffusions with random coefficients (with G. Papanicolaou).- Ohrnstein-Uhlenbeck process in a random potential (with G. Papanicolaou).- Large deviations for random walks in a random environment.- Random walks in a random environment.- Stochastic homogenization of Hamilton-Jacobi-Bellman equations (with E. Kosygina and F. Rezakhanlou).- Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium (with E. Kosygina).- Behavior of the solution of a random semilinear heat equation (with N. Zygouras).
