9704744 Rosinski Professor Jan Rosinski intends to investigate representations of non-Gaussian infinitely divisible processes under a general framework of stationarity with respect to groups of transformations. To accomplish this goal, he proposes to develop new connections between the theory of stochastic processes and ergodic theory, group representations, particularly those induced in the sense of Mackey, and functional analysis. These general results can be applied in the structural analysis of stationary, self-similar, and isotropic infinitely divisible random fields. He also intends to continue research on asymptotic independence of stochastic processes, sample path continuity, and multiple stochastic integrals. Infinitely divisible random processes appear naturally in many areas of theoretical and applied probability, communications, networking, mathematical finance, and statistics. Roughly speaking, a process is infinitely divisible if its behavior is determined by a large number of mutually independent random factors. Stationarity is a notion describing statistical symmetries of a random process. Stationary infinitely divisible processes, which may exhibit high variability, are not well understood at present because the traditional methodology of Gaussian processes is not applicable here. This project is intended to develop tools and methods for analysis of infinitely divisible processes which can be used in modeling of highly variable phenomena.
