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Diffusion processes fnd Riemannian geometry

S. A. Molchanov


Abstract: This paper studies the asymptotic behaviour as $t\to 0$ of the transition density of a diffusion process on a smooth manifold. The results are stated in the language of differential geometry. We look at applications of the asymptotic formulae to the local structure of diffusion processes and to spectral theory.

UDC: 519.9+513.8

MSC: 58J65, 58J60, 60J60, 58J37

Received: 12.03.1974

 English version: Russian Mathematical Surveys, 1975, 30:1, 1–63

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