Bismut type formulae for diffusion semigroups on Riemannian manifolds

Ana Bela Cruzeiro; Xicheng Zhang

doi:10.1007/s11118-006-9010-8

Bismut type formulae for diffusion semigroups on Riemannian manifolds

Ana Bela Cruzeiro^*, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Applying the stochastic calculus of variations on frame bundles along tangent processes, we derive Bismut type formulae for the derivatives of diffusion semigroups on Riemannian manifold in both variables. We also obtain the Bismut formulae expressed in terms of the Ricci and torsion tensors for the connection with torsion.

Original language	English
Pages (from-to)	121-130
Number of pages	10
Journal	Potential Analysis
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s11118-006-9010-8
Publication status	Published - Sept 2006
Externally published	Yes

Keywords

Bismut formulae
Diffusion semigroups
Heat kernel derivatives

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10.1007/s11118-006-9010-8

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title = "Bismut type formulae for diffusion semigroups on Riemannian manifolds",

abstract = "Applying the stochastic calculus of variations on frame bundles along tangent processes, we derive Bismut type formulae for the derivatives of diffusion semigroups on Riemannian manifold in both variables. We also obtain the Bismut formulae expressed in terms of the Ricci and torsion tensors for the connection with torsion.",

keywords = "Bismut formulae, Diffusion semigroups, Heat kernel derivatives",

author = "Cruzeiro, {Ana Bela} and Xicheng Zhang",

year = "2006",

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doi = "10.1007/s11118-006-9010-8",

language = "English",

volume = "25",

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AU - Cruzeiro, Ana Bela

AU - Zhang, Xicheng

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AB - Applying the stochastic calculus of variations on frame bundles along tangent processes, we derive Bismut type formulae for the derivatives of diffusion semigroups on Riemannian manifold in both variables. We also obtain the Bismut formulae expressed in terms of the Ricci and torsion tensors for the connection with torsion.

KW - Bismut formulae

KW - Diffusion semigroups

KW - Heat kernel derivatives

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U2 - 10.1007/s11118-006-9010-8

DO - 10.1007/s11118-006-9010-8

M3 - Article

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VL - 25

SP - 121

EP - 130

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Bismut type formulae for diffusion semigroups on Riemannian manifolds

Abstract

Keywords

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