Diffusion processes on complete riemannian manifolds |
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| Authors: | Zhongmin Qian |
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| Institution: | (1) Department of Applied Mathematics, Shanghai Institute of Railway Technology, 200333 Shanghai, China |
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| Abstract: | In this paper, a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established. Applying it to the heat kernel estimate of the operator 1/2  +b, we obtain the Aronson's estimate for the operator 1/2 +b, which can be regarded as an extension of Peter Li and S.T. Yau's heat kernel estimate for the Laplace-Beltrami operator.This project is partially supported by the National Natural Science Foundation of China. |
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| Keywords: | Complete Riemannian manifold conditional Riemannian Brownian motion diffusion heat kernel Laplace-Beltrami operator Ricci curvature semimartingale |
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