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Stochastic oscillatory integrals with quadratic phase function and Jacobi equations
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  • Published: June 1999

Stochastic oscillatory integrals with quadratic phase function and Jacobi equations

  • S. Taniguchi1 

Probability Theory and Related Fields volume 114, pages 291–308 (1999)Cite this article

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Abstract.

An evaluation of a stochastic oscillatory integral with quadratic phase function and analytic amplitude function is given by using solutions of Jacobi equations. The evaluation will be obtained as an application of real change of variable formulas and holomorphic prolongations of analytic functions on a real Wiener space. On the way we shall see how a Jacobi equation appears in the evaluation by using the Malliavin calculus.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan (e-mail: taniguch@math.kyushu-u.ac.jp), , , , , , JP

    S. Taniguchi

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  1. S. Taniguchi
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Received: 27 July 1998 / Revised version: 14 October 1998

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Taniguchi, S. Stochastic oscillatory integrals with quadratic phase function and Jacobi equations. Probab Theory Relat Fields 114, 291–308 (1999). https://doi.org/10.1007/s004400050227

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  • Issue Date: June 1999

  • DOI: https://doi.org/10.1007/s004400050227

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  • Mathematics Subject Classification (1991): 60H07, 60H05, 60G30
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