ON THE JACOBI FIELD APPROACH TO STOCHASTIC OSCILLATORY INTEGRALS WITH QUADRATIC PHASE FUNCTION

Setsuo TANIGUCHI

doi:10.2206/kyushujm.61.191

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

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ON THE JACOBI FIELD APPROACH TO STOCHASTIC OSCILLATORY INTEGRALS WITH QUADRATIC PHASE FUNCTION

Setsuo TANIGUCHI

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Keywords: quadratic Wiener functional, stochastic oscillatory integral, Jacobi fields, Volterra operator

JOURNAL FREE ACCESS

2007 Volume 61 Issue 1 Pages 191-208

DOI https://doi.org/10.2206/kyushujm.61.191

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Abstract

The approach taking advantage of Jacobi fields to represent explicitly stochastic oscillatory integrals with quadratic phase function, introduced by Ikeda, Kusuoka, and Manabe, is completed in the general scheme and is testified in several examples.

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