By S. R. Varadhan
Prokhorov’s thesis, which dealt with weak convergence of probability measures on complete separable metric (Polish) spaces, continues to play an important role in the theory of stochastic processes. Prokhorov’s compactness criterion for families of probability measures on a Polish space is a standard tool in proving limit theorems for stochastic processes. He made important contributions to probability as well as to statistics.
A member of the Russian Academy of Sciences, Prokhorov spent most of his professional life at the Steklov Institute of Mathematics, where he succeeded Kolmogorov as head of the probability section. He was the recipient of many honors, including the Lenin Prize.
For more than 40 years, Prokhorov was editor-in-chief of Teoriya Veroyatnostei i ee Primeneniya, the Soviet–Russian journal in applied probability that SIAM has long published in translation as Theory of Probability and Its Applications.
S. R. Varadhan is Frank Jay Gould Professor of Science at Courant Institute of Mathematical Sciences, New York University.