Niveau: Supérieur, Doctorat, Bac+8
INCREASING CONVEX MONOTONE MARKOV CHAINS: THEORY, ALGORITHM AND APPLICATIONS? MOUAD BEN MAMOUN†‡ , ANA BUSˇIC† , JEAN-MICHEL FOURNEAU†, AND NIHAL PEKERGIN† Abstract. We develop theoretical and algorithmic aspects of discrete-time Markov chain com- parison with the increasing convex order. This order is based on the variability of the process and it is expected that one can get more accurate bounds with such an order although the monotonicity property is more complex. We give a characterization for finite state space to obtain an algebraic de- scription which is suitable for an algorithmic framework. We develop an algorithm and we introduce some applications related to the worst case stochastic analysis when some high level information is known, but not the complete structure of the chain. Key words. Markov chains, stochastic bounds AMS subject classifications. 60E15, 60J22, 15A51 1. Introduction. Comparison techniques have gained an increasing popularity in the study of stochastic processes [23]. These techniques may be related to various mathematical theory (stochastic ordering, polyhedral theory, Markov chain decision process, stochastic recurrence equation). In the context of numerical analysis of Markov chains, the first idea was to analyze systems which are too difficult for numerical analysis. One can compare a chain of the model with another one which is simpler to solve. A recent survey [16] presents several solutions that we can group into two key ideas: reduction of the state space or using an ad hoc structure, the numerical analysis of which is simpler.
- increasing convex monotone
- order
- however
- icx
- all increasing
- con- tinuous time
- markov chains