Professor Emeritus of Applied Mathematics and Engineering and L. Herbert Ballou University Professor Emeritus


Kushner received the Ph.D. in Electrical Engineering from the University of Wisconsin in 1958. He worked at Lincoln Laboratories and RIAS before coming to Brown in 1964 with the group that formed the Lefschetz Center for Dynamical Systems. He is a former director of that center as well as a former chairman of the Applied Mathematics Department, and is currently a University Professor Emeritus.

Since then, in ten books and well over two hundred papers, he has
established a substantial part of modern stochastic systems theory.
These include seminal developments of stochastic stability for both
Markovian and non-Markovian systems, optimal nonlinear filtering and effective algorithms for approximating optimal nonlinear filters, stochastic variational methods and the stochastic maximum principle, numerical methods for jump-diffusion type control and game
problems (the current methods of choice), efficient numerical methods for Markov chain models, methods for singularly perturbed stochastic systems, an extensive development of controlled stochastic networks such as queueing/communications systems under conditions of heavy traffic, methods for the analysis and approximation of systems driven by wideband noise, large-deviation methods for control problems with small noise effects, stochastic distributed and delay systems, and nearly optimal control and filtering for non-Markovian systems. His work on stochastic approximations and recursive
algorithms has set much of the current framework, and he has contributed heavily to applications of control methods to communications problems.

Brown Affiliations

Research Areas