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.​​