[1] He is regarded as one of the fundamental contributors to the theory of diffusion processes with an orientation towards the refinement and further development of Itô’s stochastic calculus.

He received his doctorate from Indian Statistical Institute in 1963 under C R Rao,[7][8] who arranged for Andrey Kolmogorov to be present at Varadhan's thesis defence.

[10] Since 1963, he has worked at the Courant Institute of Mathematical Sciences at New York University, where he was at first a postdoctoral fellow (1963–66), strongly recommended by Monroe D Donsker.

In an article in the Notices of the American Mathematical Society, Stroock recalls these early years: Varadhan, whom everyone calls Raghu, came to these shores from his native India in the fall of 1963.

Yet despite the somewhat humble surroundings, from these offices flowed a remarkably large fraction of the post-war mathematics of which America is justly proud.Varadhan is currently a professor at the Courant Institute.