TY - JOUR
T1 - Convergence of non-symmetric diffusion processes on RCD spaces
AU - Suzuki, Kohei
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.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-018-1398-7
DO - 10.1007/s00526-018-1398-7
M3 - Article
AN - SCOPUS:85050534008
VL - 57
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 5
M1 - 120
ER -