## Journal of the Mathematical Society of Japan

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 January 2017

https://projecteuclid.org/euclid.jmsj/1484730020

Digital Object Identifier
doi:10.2969/jmsj/06910111

Mathematical Reviews number (MathSciNet)
MR3597549

Zentralblatt MATH identifier
1362.32024

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1484730020

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