PATH INTEGRAL FORMULAS FOR HEAT KERNELS AND THEIR DERIVATIVES

被引：21

作者：

NORRIS, JR

机构：

[1] Statistical Laboratory, University of Cambridge, Cambridge, CB2 1SB

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1993年 / 94卷 / 04期

关键词：

Mathematics Subject Classification: 58G32;

D O I：

10.1007/BF01192562

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The heat kernel and its derivatives of a vector Laplacian on the sections of a bundle over a compact Riemannian manifold are expressed as products of the scalar heat kernel of the manifold and path integrals over the Brownian bridge. The small-time asymptotics of these integrals are computed.

引用

页码：525 / 541

页数：17

共 9 条

[1]

Bismut J.-M., 1984, PROGR MATH, V45

[2]

BISMUT JM, 1981, PROBAB THEORY REL, V56, P469

[3] FLOWS OF STOCHASTIC DYNAMICAL-SYSTEMS - THE FUNCTIONAL ANALYTIC APPROACH [J].

CARVERHILL, AP ;

ELWORTHY, KD .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1983, 65 (02) :245-267

[4]

Elworthy K.D., 1982, LONDON MATH SOC LECT, V70

[5]

ELWORTHY KD, 1992, PROGR PROBAB, V27, P37

[6] ON THE PARABOLIC KERNEL OF THE SCHRODINGER OPERATOR [J].

LI, P ;

YAU, ST .

ACTA MATHEMATICA, 1986, 156 (3-4) :153-201

[7]

NORRIS J, 1986, LECT NOTES MATH, V1204, P101

[8]

NORRIS JR, COMPLETE DIFFERENTIA

[9] ASYMPTOTIC PROBABILITIES AND DIFFERENTIAL EQUATIONS [J].

VARADHAN, SR .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1966, 19 (03) :261-&

← 1 →