On Markov stability

Uniform Stability of Markov Chains*

By deriving a new set of tight perturbation bounds, it is shown that all stationary probabilities of a finite irreducible Markov chain react essentially in the same way to perturbations in the transition probabilities. In particular, if at least one stationary probability is insensitive in a relative sense, then all stationary probabilities must be insensitive in an absolute sense. New measures...

Spectral stability of Markov systems

For a class of semigroups of stochastic dynamical systems, x 7→ Px, where x denotes a state and Px the state probability transition, we relate its spectral stability with the combinatorial stability of the underlying non-deterministic dynamics, associated to the point-set map x 7→ supp(Px).

Some Remarks on Uniformly Bounded Markov Chains: Stability Analysis

Since the appearance of a paper by Carleial and Hellman [2] in 1975, it is known that the bistable behavior of the ALOHA system is associated with a bimodal shape of the backlog steady-state disbibution. In this paper, we generalize the problem and ask under what conditions a one-dimensional Markov Chain possesses a multimodal steady-state distribution. We restrict our analysis to wtiformly bou...

Note on stability estimation in average Markov control processes

On Stability of Nonlinear Ar Processes with Markov Switching

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibil...