1 Preliminaries Let fX t g be a discrete-time stochastic process. Throughout, we will assume that any process fX t g is indexed by the integers or some subset of the integers (for example, the positive integers). In practice, we observe a nite length sample (or time series) X 1 ; ; X n from fX t g. (In this presentation, we will distinguish between a stochastic process fX t g and a nite time se...

We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a nontrivial stationary state. We discuss the results and in particular draw from our results some general features shared by these distributions in realistic ...

We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the singleserver retrial queue analyzed in Keilson and Servi [1]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues ([1] and [2]). The main contribution of the present paper is the derivation of the explicit form of the stationary system...

the existence of shift for periodically correlated processes and its boundedness are investigated. spectral criteria for these non-stationary processes to have such shifts are obtained.