Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
A NEW CLASS OF AMPLITUDE FUNCTIONS FOR THE STATIONARY PHASE METHOD ON AN ABSTRACT WIENER SPACE
Setsuo TANIGUCHI
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2015 Volume 69 Issue 1 Pages 219-228

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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.

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© 2015 Faculty of Mathematics, Kyushu University
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