| Abstract: | We obtain, using large deviations principles, full asymptotic expansions of functionals of Laplace type on Wiener space for general (i.e. degenerate) diffusions extending the results of Schilder 12], Azencott 2] and Doss 7, 20]. The variational hypothesis (non degeneracy of the minima) used here is shown to be optimal. The first term of the expansion is explicitly computed. Using the integration by parts of Malliavin calculus the stationary phase method is also developed. The results of this paper are the basic fact used (in 5]) to obtain the asymptotic expansion for small time of the density of a degenerate diffusion, they are also relevant for semi-classical expansions |
