Radial processes on RCD                         ⁎                         (K,N) spaces

Kazumasa Kuwada; Kazuhrio Kuwae

doi:10.1016/j.matpur.2018.12.008

Radial processes on RCD ^⁎ (K,N) spaces

Kazumasa Kuwada, Kazuhrio Kuwae

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

4 Citations (Scopus)

Abstract

In this paper, we show a stochastic expression for the radial processes of Brownian motions on RCD ^⁎ (K,N)-spaces. It corresponds to the one on Riemannian manifolds. The expression holds for all starting points without exceptional sets. It can be extended beyond the hitting time to the reference point provided the reference point is sufficiently regular. We further prove that the regularity condition is satisfied for almost every reference point. Our results extend the comparison theorems over Alexandrov spaces proved in [36,29].

Original language	English
Pages (from-to)	72-108
Number of pages	37
Journal	Journal des Mathematiques Pures et Appliquees
Volume	126
DOIs	https://doi.org/10.1016/j.matpur.2018.12.008
Publication status	Published - 2019 Jun
Externally published	Yes

Keywords

Alexandrov space
Dirichlet form
Laplacian comparison theorem
RCD (K,N)-space
Radial process
Riemannian manifold

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1016/j.matpur.2018.12.008

Cite this

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title = " Radial processes on RCD ⁎ (K,N) spaces ",

abstract = " In this paper, we show a stochastic expression for the radial processes of Brownian motions on RCD ⁎ (K,N)-spaces. It corresponds to the one on Riemannian manifolds. The expression holds for all starting points without exceptional sets. It can be extended beyond the hitting time to the reference point provided the reference point is sufficiently regular. We further prove that the regularity condition is satisfied for almost every reference point. Our results extend the comparison theorems over Alexandrov spaces proved in [36,29]. ",

keywords = "Alexandrov space, Dirichlet form, Laplacian comparison theorem, RCD (K,N)-space, Radial process, Riemannian manifold",

author = "Kazumasa Kuwada and Kazuhrio Kuwae",

note = "Funding Information: Supported in part by Japan Society for the Promotion of Science Grant-in-Aid for Young Scientist (KAKENHI) 26707004.Supported in part by Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (KAKENHI) 17H02846. The authors would like to tell their sincere gratitude to the anonymous referee. His/Her comments help to improve the quality of this paper very much. Publisher Copyright: {\textcopyright} 2019 Elsevier Masson SAS",

year = "2019",

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doi = "10.1016/j.matpur.2018.12.008",

language = "English",

volume = "126",

pages = "72--108",

journal = "Journal des Mathematiques Pures et Appliquees",

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T1 - Radial processes on RCD ⁎ (K,N) spaces

AU - Kuwada, Kazumasa

AU - Kuwae, Kazuhrio

N1 - Funding Information: Supported in part by Japan Society for the Promotion of Science Grant-in-Aid for Young Scientist (KAKENHI) 26707004.Supported in part by Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (KAKENHI) 17H02846. The authors would like to tell their sincere gratitude to the anonymous referee. His/Her comments help to improve the quality of this paper very much. Publisher Copyright: © 2019 Elsevier Masson SAS

PY - 2019/6

Y1 - 2019/6

N2 - In this paper, we show a stochastic expression for the radial processes of Brownian motions on RCD ⁎ (K,N)-spaces. It corresponds to the one on Riemannian manifolds. The expression holds for all starting points without exceptional sets. It can be extended beyond the hitting time to the reference point provided the reference point is sufficiently regular. We further prove that the regularity condition is satisfied for almost every reference point. Our results extend the comparison theorems over Alexandrov spaces proved in [36,29].

AB - In this paper, we show a stochastic expression for the radial processes of Brownian motions on RCD ⁎ (K,N)-spaces. It corresponds to the one on Riemannian manifolds. The expression holds for all starting points without exceptional sets. It can be extended beyond the hitting time to the reference point provided the reference point is sufficiently regular. We further prove that the regularity condition is satisfied for almost every reference point. Our results extend the comparison theorems over Alexandrov spaces proved in [36,29].

KW - Alexandrov space

KW - Dirichlet form

KW - Laplacian comparison theorem

KW - RCD (K,N)-space

KW - Radial process

KW - Riemannian manifold

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