Journal of the Mathematical Society of Japan

A construction of diffusion processes associated with sub-Laplacian on CR manifolds and its applications

Hiroki KONDO and Setsuo TANIGUCHI

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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.

Article information

J. Math. Soc. Japan, Volume 69, Number 1 (2017), 111-125.

First available in Project Euclid: 18 January 2017

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Zentralblatt MATH identifier

Primary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
Secondary: 60J60: Diffusion processes [See also 58J65]

CR manifold stochastic differential equation Malliavin calculus partial hypoellipticity Dirichlet problem


KONDO, Hiroki; TANIGUCHI, Setsuo. A construction of diffusion processes associated with sub-Laplacian on CR manifolds and its applications. J. Math. Soc. Japan 69 (2017), no. 1, 111--125. doi:10.2969/jmsj/06910111.

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