Functional law of iterated logarithm for additive functionals of reversible Markov processes (Q1568246)

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.