Michael Marcus, Professor of Mathematics at The Graduate Center and City College, is currently studying the relationship between Gaussian processes and the local times of symmetric Markov processes and, for symmetric Markov processes for which local times do not exist, the relationship between continuous additive functionals on spaces of measures, which serve as substitutes for local times, and corresponding families of Gaussian chaoses.
In 1986, Professor Marcus' research took an exciting new direction. Impressed by a recent result that related local times of Levy processes to stationary Gaussian processes, he set out to explore this unexpected relationship between these seemingly different classes of stochastic processes. Using an isomorphism theorem of E. Dynkin, in collaboration with Jay Rosen, Professor of Mathematics at The Graduate Center and the College of Staten Island, he showed that many sample path properties of strongly symmetric Markov processes are the same as those of related Gaussian processes.
Professor Marcus began his research on sample path properties of stationary Gaussian processes in 1965. This area received a great deal of attention internationally and by the end of the 1980s many results had been obtained. Using the insights he developed studying Gaussian processes he made substantial contributions in many significant areas of probability that demonstrated the centrality of Gaussian processes in the theory of probability.
Public and private agencies have recognized the significance of his research. IN 1993 he received a Guggenheim Foundation fellowship. The National Science Foundation has supported him since 1968. The last three, three-year awards on his proposal, Stochastic Processes, in collaboration with Jay Rosen, cover the period 1995-2004. Some of these awards include full fellowships for graduate students. Marcus and Rosen also use these funds to sponsor a weekly seminar in probability at The Graduate Center, with speakers from both CUNY and other major universities and colleges in the northeast.