Functional law of iterated logarithm for additive functionals of reversible Markov processes
The functional law of iterated logarithm or the strong invariance principle of Strassen for an additive functional \((A_t)\) of a reversible Markov process is obtained. The results hold under the minimal condition that \(\exists \lim_{t\to \infty}EA_t^2/t\) in \(R.\) The author uses the forward-backward martingale decomposition technique and limit theorems for martingales. An extension of the functional central limit theorem of Kipnis and Varadhan is obtained.
forward-backward martingale decomposition
scientific article; zbMATH DE number 1462505