A NEW CLASS OF AMPLITUDE FUNCTIONS FOR THE STATIONARY PHASE METHOD ON AN ABSTRACT WIENER SPACE

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Abstract

A stochastic oscillatory integral is a probabilistic counterpart to a Feynman path integral, and the stationary phase method for stochastic oscillatory integrals relates to the semi-classical limits in the Feynman path integral theory. A complete stationary phase method for stochastic oscillatory integrals has not been achieved yet. In this paper, a new class of amplitude functions of stochastic oscillatory integrals is introduced, and it is shown that the stationary phase method works for the class.

Journal

  • Kyushu Journal of Mathematics

    Kyushu Journal of Mathematics 69(1), 219-228, 2015

    Faculty of Mathematics, Kyushu University

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