Citation
A. Ancona et al., Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths, ANN PROBAB, 27(2), 1999, pp. 970-989
Citations number
18
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798
→ ACNP
Volume
27
Issue
2
Year of publication
1999
Pages
970 - 989
Database
ISI
SICI code
0091-1798(199904)27:2<970:CEACOD>2.0.ZU;2-K
Abstract
Let {X-n} be a transient reversible Markov chain and let f be a function on
the state space with finite Dirichlet energy. We prove crossing inequaliti
es for the process (f(X-n)}(n greater than or equal to 1) and show that it
converges almost surely and in L-2. Analogous results are also established
for reversible diffusions on Riemannian manifolds.