On monotone Markov chains and properties of monotone matrix roots

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...

Income Distribution Dynamics: Monotone Markov Chains Make Light Work By

Strong stationary duality for Möbius monotone Markov chains

For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an interpretation for unreliable networks of queues.

Monotone dependence in graphical models for multivariate Markov chains

We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according ...

Optimal guarding of polygons and monotone chains

In this paper we study several problems concerning the guarding of a polygon or a x-monotone polygonal chain P with n vertices from a set of points lying on it. Our results are: (1) An O(n logn) time sequential algorithm for computing the shortest guarding boundary chain of a polygon P. (2) An O(n logn) time sequential algorithm for computing the smallest set of consecutive edges guarding a pol...