Degenerate processes killed at the boundary of a domain (2103.08534v4)

Abstract: We investigate certain properties of degenerate Feller processes that are killed when exiting a relatively compact set. Our main result provides general conditions ensuring that such a process possesses a (possibly non unique) quasi stationary distribution. Conditions ensuring uniqueness and exponential convergence are discussed. The results are applied to nonelliptic and hypoelliptic stochastic differential equations.