Mathematical Sciences: Brownian Motion and Related Stochastic Processes

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The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Particular subjects for study are the following: interval partitions associated with a subordinator, multiple points of Brownian motion in dimensions 2 and 3, Tsirelson's equations in discrete time, non-canonical decompositions of Brownian motion, the Ciesielski-Taylor identities in law, multivariate Cauchy variables and affine decompositions of a stable variable of index (1/2), intertwinings of Markov processes, and characterization of the Brownian filtration. The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Stochastic processes represent an important area of research in probability theory.