### 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.

Original language | English |
---|---|

Pages (from-to) | 291-308 |

Number of pages | 18 |

Journal | Probability Theory and Related Fields |

Volume | 114 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1999 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Stochastic oscillatory integrals with quadratic phase function and Jacobi equations.** / Taniguchi, Setsuo.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 114, no. 3, pp. 291-308. https://doi.org/10.1007/s004400050227

}

TY - JOUR

T1 - Stochastic oscillatory integrals with quadratic phase function and Jacobi equations

AU - Taniguchi, Setsuo

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033163702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033163702&partnerID=8YFLogxK

U2 - 10.1007/s004400050227

DO - 10.1007/s004400050227

M3 - Article

AN - SCOPUS:0033163702

VL - 114

SP - 291

EP - 308

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -