This award will support a research collaboration between Professor J. L. Menaldi of Wayne State University and Professor Maria Garroni of the University of Rome, Italy. The investigators intend to study various research problems in stochastic control and related classic analysis. Their study should lead to an enhancement of our basic theoretical knowledge and expand the range of applicability of several areas of modern stochastic control theory. The proposed project builds on a successful prior collaboration and has the potential to make a solid contribution to the field. For this study the underlying probabilistic models are described by stochastic differential equations related to diffusion, possibly with jumps, in finite dimensions. Mathematically this is a relatively well-developed area that permits an in-depth analysis of model problems. For optimal control, a dynamic programming principle is adopted as a unifying approach. This gives rise to nonlinear partial differential equations, and variational or quasi-variational inequalities.
