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

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<p>A diffusion process associated with the real sub-Laplacian Δb, the real part of the complex Kohn–Spencer Laplacian □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 Δb are studied in a probabilistic manner. Moreover, distributions of stochastic line integrals along the diffusion process will be investigated.</p>

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