Abstract
We prove results on exact asymptotics as for the means and probabilities , where , , is an -dimensional Wiener process, is a positive continuous function (potential) satisfying certain conditions, , and are prescribed vectors. The results are obtained by a new method developed in this paper, the Laplace method for the occupation time of a multi-dimensional Wiener process. We consider examples of monomial and radial potentials and prove results on exact asymptotics of small deviations for the probabilities as with a fixed .
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