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 |
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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 journal › Article
}
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.
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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 -