We extend a result by Cavazos-Cadena and Lasserre on the existence of strong 1-optimal stationary policies in Markov decision chains with countable state spaces, uniformly ergodic transition probabilities and bounded costs to a larger class of models with unbounded costs and the so-called...

We extend a result by Cavazos-Cadena and Lasserre on the existence of strong 1-optimal stationary policies in Markov decision chains with countable state spaces, uniformly ergodic transition probabilities and bounded costs to a larger class of models with unbounded costs and the so-called...

The aim of this paper is to solve the basic stochastic shortest-path problem (SSPP) for Markov chains (MCs) with countable state space and then apply the results to a class of nearest-neighbor MCs on the lattice state space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb Z \times \mathbb Z $$</EquationSource> </InlineEquation> whose only moves are one step up,...</equationsource></inlineequation>

The aim of this paper is to investigate the Lagrangian approach and a related Linear Programming (LP) that appear in constrained Markov decision processes (CMDPs) with a countable state space and total expected cost criteria (of which the expected discounted cost is a special case). We consider...

The aim of this paper is to investigate the Lagrangian approach and a related Linear Programming (LP) that appear in constrained Markov decision processes (CMDPs) with a countable state space and total expected cost criteria (of which the expected discounted cost is a special case). We consider...

The aim of this paper is to solve the basic stochastic shortest-path problem (SSPP) for Markov chains (MCs) with countable state space and then apply the results to a class of nearest-neighbor MCs on the lattice state space $$\mathbb Z \times \mathbb Z $$ whose only moves are one step up, down,...

Abstract In this paper we give sufficient conditions for solving two-person zero sum stopping games. These are games where the strategy set of the two players are stopping times of a diffusion X . Our method is based on the study of harmonic functions for the diffusion and it is similar to the...