The principal investigator and his graduate students study martingales and related classes of stochastic processes, estimates on the size of stochastic integrals, the behavior of Fourier series in spaces of high dimension, and the relation of diffusions and curvature on manifolds. The focus is on concrete problems whose solutions are applicable in statistical and mathematical analysis of the kind arising in some parts of economics, the physical and natural sciences, and in technology. At the same time, the principal investigator is developing general methods that may help to solve some of the concrete problems not yet foreseen.
