Atsushi Takeuchi: Asymptotic behavior of densities for stochastic functional differential equations

Consider stochastic functional differential equations depending on whole past histories in a finite time interval, which determine non-Markovian processes. Under the uniformly elliptic condition on the diffusion terms, the solution admits a smooth density with respect to the Lebesgue measure. In this talk, we shall study the large deviations for the solution process, and the asymptotic behavior of the density. The Malliavin calculus plays a crucial role in our argument.