Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths
The authors establish a crossing estimate for a Dirichlet function \(f\) along the path of a transient reversible Markov chain \(\{X_n\}\) and prove that the process \(\{f(X_n)\): \(n\geq 1\}\) converges almost surely and in \(L^2\). Similar results are also established for a transient symmetric diffusion on a Riemannian manifold. Results on crossing estimates are recently generalized to symmetric right Markov processes by \textit{Z.-Q. Chen, P. Fitzsimmons} and \textit{R. Song} [``Crossing estimates for symmetric Markov processes''].
scientific article; zbMATH DE number 1359660
scientific article