Variational principles for asymptotic variance of general Markov processes (Q2690111)

This work establishes, under a general sectorial condition and \(L^2\) ergodicity, a variational representation of the asymptotic variance of ergodic averages of Markov processes. This extends the classical result known for reversible processes. This formulation is then used to compare different processes, and in particular to prove that the addition of a divergence-free drift to a reversible Langevin diffusion can only decrease the asymptotic variance.