New Perspectives on Random Fields with Applications

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0404729Khoshnevisan One of the primary concerns of this project is to develop a systematic geometrical analysis of random fields. Special emphasis is placed on investigating some of the random fields that arise in pure and applied mathematics, statistics, mathematical oceanography, mathematical hydrology, and mathematical physics. This research is to gather and develop probabilistic, analytic, algebraic, and geometric tools that lead to a deeper understanding of the geometry of random fields. It is expected that the contributions of this proposal may help solve a number of long-standing open problems in the theories of Levy processes and Brownian sheet, and promote applications of such random fields in the aforementioned areas.