Mathematical Sciences: Research in Stochastic Processes

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The three general areas of research are Brownian motion on manifolds, measure valued processes, and the range of a random walk. The unifying theme among them is the study of intersection local times. The research is generalization to manifolds of the results previously obtained by the investigator. Various forms of intersection local times are used. Study of the local times for Levy processes is prompted due to the relatively recent discovery of the necessary and sufficient condition for sample continuity of a stationary Gaussian process. The isolation of the regular part of the intersection local times of higher orders lead in a normal way to the study of anticipative integrands. Various new methods developed for these integrands will contribute towards the study of the higher order intersection local times.