The principal investigator will extend his past results on sojourn times, local times and extremes of stochastic processes to the multidimensional case. The investigator has found many distributional and structural results about the above functionals in the one dimensional case. Since these processes are used extensively as models in many situations, the properties of these functionals are important from the applications point of view. A related concept is the multiplicity of values of the sample functions of stochastic processes. Properties of sets of points of multiplicity m have been studied for Markov and other processes. The investigator will extend these ideas to multi- dimensional case.
