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January, 2017 A construction of diffusion processes associated with sub-Laplacian on CR manifolds and its applications
Hiroki KONDO, Setsuo TANIGUCHI
J. Math. Soc. Japan 69(1): 111-125 (January, 2017). DOI: 10.2969/jmsj/06910111

Abstract

A diffusion process associated with the real sub-Laplacian $\Delta_b$, the real part of the complex Kohn–Spencer Laplacian $\square_b$, on a strictly pseudoconvex CR manifold is constructed via the Eells–Elworthy–Malliavin method by taking advantage of the metric connection due to Tanaka and Webster. Using the diffusion process and the Malliavin calculus, the heat kernel and the Dirichlet problem for $\Delta_b$ are studied in a probabilistic manner. Moreover, distributions of stochastic line integrals along the diffusion process will be investigated.

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Hiroki KONDO. Setsuo TANIGUCHI. "A construction of diffusion processes associated with sub-Laplacian on CR manifolds and its applications." J. Math. Soc. Japan 69 (1) 111 - 125, January, 2017. https://doi.org/10.2969/jmsj/06910111

Information

Published: January, 2017
First available in Project Euclid: 18 January 2017

zbMATH: 1362.32024
MathSciNet: MR3597549
Digital Object Identifier: 10.2969/jmsj/06910111

Subjects:
Primary: 58J65
Secondary: 60J60

Rights: Copyright © 2017 Mathematical Society of Japan

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Vol.69 • No. 1 • January, 2017
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