We consider an investment model which generalizes a number of models that have been studied in the literature. The model involves entry and exit decisions as well as decisions relating to production scheduling. We then address the problem of its valuation from the standpoint of the dynamic programming approach. Our analysis results in a closed form analytic solution that can take qualitatively different forms depending on parameter values.

We define a class of anticipative flows on Poisson space and compute its Radon-Nikodym derivative. This result is applied to statistical testing in an anticipative queueing problem.

We consider a network traffic model consisting of an infinite number of sources linked to a server. Sources initiate transmissions to the server at Poisson time points. The duration of each transmission has a heavy-tailed distribution. We show that suitable scalings of the traffic process converge to a totally skewed stable Lévy motion in Skorohod space, equipped with the Skorohod M1 topology. This allows us to prove a heavy-traffic theorem for a single-server fluid model.

In a recent paper [4] it was shown that, for an absorbing Markov chain where absorption is not guaranteed, the state probabilities at time t conditional on non-absorption by t generally depend on t. Conditions were derived under which there can be no initial distribution such that the conditional state probabilities are stationary. The purpose of this note is to show that these conditions can be relaxed completely: we prove, once and for all, that there are no circumstances under which a quasistationary distribution can admit a stationary conditional interpretation.

Consider a janken game (scissors-paper-rock game) started by n players such that (1) the first round is played by n players, (2) the losers of each round (if any) retire from the rest of the game, and (3) the game ends when only one player (winner) is left. Let Wn be the number of rounds played through the game. Among other things, it is proved that (2/3)nWn is asymptotically (as n → ∞) distributed according to the exponential distribution with mean ⅓, provided that each player chooses one of the three strategies (scissors, paper, rock) with equal probability and independently from other players in any round.