Previous authors have considered optimal stopping problems driven by the running maximum of a spectrally negative Lévy process as well one-dimensional diffusion; see e.g. Kyprianou and Ott (2014); (2013); Alvarez Matomäki Guo Shepp (2001); Pedersen (2000); Gapeev (2007). Many aforementioned results are either implicitly or explicitly dependent on Peskir’s maximality principle, cf. (Peskir, 1998...

In this paper we consider two-player partial-information games on Markov chains. These are games in which two players are able to influence the state transitions in a Markov chain by taking appropriate actions. Each player attempts to minimize its own cost that is additive over time with the incremental costs depending on the state of the Markov chain and the actions taken by the players. We co...

We study the performance of discrete-time consensus protocols in the presence of additive noise. When the consensus dynamic corresponds to a reversible Markov chain, we give an exact expression for a weighted version of steady-state disagreement in terms of the stationary distribution and hitting times in an underlying graph. We then show how this result can be used to characterize the noise ro...

The classical model of Markov decision processes with costs or rewards, while widely used to formalize optimal decision making, cannot capture scenarios where there are multiple objectives for the agent during the system evolution, but only one of these objectives gets actualized upon termination. We introduce the model of Markov decision processes with alternative objectives (MDPAO) for formal...