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-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.

14 pages

References in corpus (1)

• Weak Convergence to Brownian Motion on Sub-Riemannian Manifolds

Cited by in corpus (2)

• Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus
• A concrete approach to diagonal short time asymptotics of heat kernels associated with sub-Laplacian on CR manifolds