We investigate the question of when sampling a stochastic process X={X(t): t[greater-or-equal, slanted]0} at the times of an independent point process [psi] leads to the same empirical distribution as the time-average limiting distribution of X. Two main cases are considered. The first is...

Let X={X(t):t[greater-or-equal, slanted]0} be a positive recurrent synchronous process (PRS), that is, a process for which there exists an increasing sequence of random times [tau]={[tau](k)} such that for each k the distribution of is the same and the cycle lengths have finite first moment....

We study the tail asymptotics of the r.v. X(T) where {X(t)} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail...

We present, in discrete time, general-state-space dualities between content and insurance risk processes that generalize the stationary recursive duality of Asmussen and Sigman (1996, Probab. Eng. Inf. Sci. 10, 1-20) and the Markovian duality of Siegmund (1976, Ann. Probab. 4, 914-924) (both of...

The stability of open Jackson networks is established where service times are i.i.d. general distribution, exogeneous interarrival times are i.i.d. general distribution, and the routing is Markovian. The service time distributions are only required to have finite first moment. The system is...

The inventory equation, Z(t) = X(t) + L(t), where X = X(t):t = 0 is a given netput process and L(t):t = 0 is the corresponding lost potential process, is explored in the general case when X is a negative drift stochastic process that has asymptotically stationary increments. Our results show...