This paper elucidates the connection between stationary symmetric α-stable processes with 0 < α < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that a necessary and sufficient for a stationary stable process to be ergodic is that its p...

m-dependent stationary infinitely divisible sequences are characterized as a certain generalized finite moving average sequence or equivalently via the structure of their Lévy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum con...

we shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a p-invariant measure m for Q to be p-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. @ 2000 Elsevier Science Ltd. All rights reserv...

This paper studies a discrete-time total-reward Markov decision process (MDP) with a given initial state distribution. A (randomized) stationary policy can be split on a given set of states if the occupancy measure of this policy can be expressed as a convex combination of the occupancy measures of stationary policies, each selecting deterministic actions on the given set and coinciding with th...

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measures the departure of the data set from the stationary regime; it vanishes if and only if the data are stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.