In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

In this paper we study the functional central limit theorem (CLT) for stationary Markov chains with a self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n, and establish that conditional convergence in distribution of partial sums implies the functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.

The construction and properties of reversible and dynamically reversible models for finite-state Markov processes are studied. Certain results on approximating processes with rational power spectra with dynamically reversible finite-state models are also obtained.

A type of service system of particular interest in teletraffic theory has the property that calls (customers) originating from different sources have access to different subsets of a single group of devices (servers). One may or may not allow the formation of queues. Thierer [11], [12] has studied such a system with queues assuming it to be reversible. We investigate the conditions under which this assumption is exact.