Nikolay Krylov (mathematician, born 1941)

Nikolay Vasilievich Krylov (Николай Васильевич Крылов; born July 17, 1941, in Russia) is a Russian mathematician known for his contributions to the fields of stochastic analysis, partial differential equations (PDEs), and optimal control theory.

Krylov received his Ph.D. from Moscow State University under the supervision of Eugene Dynkin in 1966. He is currently a Distinguished McKnight University Professor at the University of Minnesota.

His research focuses primarily on controlled diffusion processes, stochastic differential equations, and the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations. He has made significant contributions to the regularity theory of solutions to these equations and to the development of numerical methods for their approximation.

Krylov is the author of numerous books and research articles, including "Controlled Diffusion Processes" (1980), "Nonlinear Elliptic and Parabolic Equations of the Second Order" (1987), and "Lectures on Stochastic Processes" (2018). He has received several awards and honors for his work, including the Steele Prize for Lifetime Achievement from the American Mathematical Society in 2020. His work has had a profound impact on the fields of probability theory, PDEs, and optimal control.