Existence and uniqueness of invariant measures for hypoelliptic diffusions are studied using Malliavin's criterion and coupling methods.
Sequential Bayesian filtering algorithms are developed for latent state estimation in continuous-time hidden Markov models.
We establish sample-path large deviation principles for solutions of SDEs with small noise and apply them to tail risk estimation.
A survey of BSDEs and their applications to nonlinear pricing, risk measures, and recursive utilities under model uncertainty.
We apply Malliavin calculus to derive probabilistic representations of Greeks for path-dependent options under general diffusion dynamics.