Related papers: A Note on the Stability of Monotone Markov Chains

Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…

We consider a decentralised multi-access algorithm, motivated primarily by the control of transmissions in a wireless network. For a finite single-hop network with arbitrary interference constraints we prove stochastic stability under the…

The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are…

In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative…

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…

This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…

Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…

In this paper we consider Markov chains with transition rates that depend on a small parameter $\varepsilon$. Under a mild assumption on the asymptotics of these transition rates, we describe the behavior of the chain at various…

This project is going to work with one example of stochastic matrix to understand how Markov chains evolve and how to use them to make faster and better decisions only looking to the present state of the system.

We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…

In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…

Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while…

We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…

This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…

We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…