The principal investigator will conduct research in three areas of the theory of stochastic processes. Two areas have to do with large deviation theory. The first concerns proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics", a class that includes diffusions with discontinuous drift and small diffusion coefficient as well as certain scaled queueing systems. The second area involves numerical and simulation methods. The third area of study is concerned with developing the theory and applications of the solution to the Skorokhod Problem, which is a basic and useful tool in the study of various "constrained" stochastic processes. The principal investigator will study several areas of the theory of stochastic (random) processes. One of the areas involves proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics". This class of stochastic processes is important in certain applications of stochastic control.
