Convergence of non-symmetric diffusion processes on RCD spaces

Kohei Suzuki

doi:10.1007/s00526-018-1398-7

Convergence of non-symmetric diffusion processes on RCD spaces

Kohei Suzuki

Advanced Institute for Materials Research (AIMR)

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

1 Citation (Scopus)

Abstract

We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli (Mem Am Math Soc 251(11):1–161, 2017). After constructing diffusions, we investigate conservativeness and the weak convergence of the laws of diffusions in terms of a geometric convergence of the underling spaces and convergences of the corresponding coefficients.

Original language	English
Article number	120
Journal	Calculus of Variations and Partial Differential Equations
Volume	57
Issue number	5
DOIs	https://doi.org/10.1007/s00526-018-1398-7
Publication status	Published - 2018 Oct 1

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Convergence of non-symmetric diffusion processes on RCD spaces",

abstract = "We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli (Mem Am Math Soc 251(11):1–161, 2017). After constructing diffusions, we investigate conservativeness and the weak convergence of the laws of diffusions in terms of a geometric convergence of the underling spaces and convergences of the corresponding coefficients.",

author = "Kohei Suzuki",

note = "Funding Information: Acknowledgements The author appreciates Prof. Masayoshi Takeda for suggesting constructive comments for Lyons–Zheng decompositions in the non-symmetric case. He also expresses his great appreciation to Prof. Shouhei Honda for valuable comments about the convergence of derivations. He is indebted to his wife, Anna Katharina Suzuki-Klasen for her attentive proofreading. Finally, he expresses his great appreciation to an anonymous referee for carefully reading the manuscript to this paper, and giving a number of insightful and constructive comments. This work was supported by Hausdorff Center of Mathematics in Bonn.",

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N1 - Funding Information: Acknowledgements The author appreciates Prof. Masayoshi Takeda for suggesting constructive comments for Lyons–Zheng decompositions in the non-symmetric case. He also expresses his great appreciation to Prof. Shouhei Honda for valuable comments about the convergence of derivations. He is indebted to his wife, Anna Katharina Suzuki-Klasen for her attentive proofreading. Finally, he expresses his great appreciation to an anonymous referee for carefully reading the manuscript to this paper, and giving a number of insightful and constructive comments. This work was supported by Hausdorff Center of Mathematics in Bonn.

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