On the asymptotic behaviour of the kernel associated by a degenerated diffusion. (Sur le comportement asymptotique du noyau associé à une diffusion dégénérée.) (French) Zbl 0970.35010
Summary: We consider the asymptotic behaviour for small time of the heat kernel describing the motion of a Brownian particle on a Riemannian manifold perturbed by a multiplication noise. Asymptotic expansions for the heat kernel and the trace are given and the first-order terms are explicitely calculated.
MSC:
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 53C17 | Sub-Riemannian geometry |
