Ergodic approximation of the distribution of a stationary diffusion: rate of convergence (Q433906)

The authors consider a class of Brownian ergodic diffusion processes with unique invariant distribution, drift and variance which are Lipschitz continuous functions. They study the rate of convergence to the distribution of this process, when stationary, of some weighted measures based on both the true paths and the Euler discretization scheme with decreasing step. The central limit theorems are formally established for the marginal empirical measure of these processes. The obtained results are illustrated by simulations in connection with barrier option pricing.