Isotropic transport process on a riemannian manifold

Mark A. Pinsky

doi:10.1090/S0002-9947-1976-0402957-2

Isotropic transport process on a riemannian manifold

Mark A. Pinsky^*

^*Corresponding author for this work

Mathematics

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

36 Scopus citations

Abstract

We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class C₀. The special case of a manifold of negative curvature is considered as an illustration.

Original language	English (US)
Pages (from-to)	353-360
Number of pages	8
Journal	Transactions of the American Mathematical Society
Volume	218
DOIs	https://doi.org/10.1090/S0002-9947-1976-0402957-2
State	Published - 1976

Keywords

Brownian motion
Contraction semigroup
Geodesic flow
Isotropic transport process

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1976-0402957-2

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title = "Isotropic transport process on a riemannian manifold",

abstract = "We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class C0. The special case of a manifold of negative curvature is considered as an illustration.",

keywords = "Brownian motion, Contraction semigroup, Geodesic flow, Isotropic transport process",

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T1 - Isotropic transport process on a riemannian manifold

AU - Pinsky, Mark A.

PY - 1976

Y1 - 1976

N2 - We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class C0. The special case of a manifold of negative curvature is considered as an illustration.

AB - We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class C0. The special case of a manifold of negative curvature is considered as an illustration.

KW - Brownian motion

KW - Contraction semigroup

KW - Geodesic flow

KW - Isotropic transport process

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DO - 10.1090/S0002-9947-1976-0402957-2

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SP - 353

EP - 360

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Isotropic transport process on a riemannian manifold

Abstract

Keywords

ASJC Scopus subject areas

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