Stochastic oscillatory integrals with quadratic phase function and Jacobi equations

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)291-308
Number of pages18
JournalProbability Theory and Related Fields
Volume114
Issue number3
DOIs
Publication statusPublished - Jan 1 1999

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Jacobi Equation
Oscillatory Integrals
Stochastic Integral
Evaluation
Wiener Space
Malliavin Calculus
Prolongation
Change of Variables
Analytic function
Integral

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.

In: Probability Theory and Related Fields, Vol. 114, No. 3, 01.01.1999, p. 291-308.

Research output: Contribution to journalArticle

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