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Increasing Convex Monotone Markov Chains: Theory, Algorithm and Applications

We develop theoretical and algorithmic aspects of discrete-time Markov chain comparison 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 description 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.