TY - JOUR
T1 - A construction of diffusion processes associated with sub-Laplacian on CR manifolds and its applications
AU - Kondo, Hiroki
AU - Taniguchi, Setsuo
N1 - Publisher Copyright:
©2017 The Mathematical Society of Japan.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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U2 - 10.2969/jmsj/06910111
DO - 10.2969/jmsj/06910111
M3 - Article
AN - SCOPUS:85013656521
SN - 0025-5645
VL - 69
SP - 111
EP - 125
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
IS - 1
ER -