Verifiable Conditions for the Irreducibility and Aperiodicity of Markov Chains by Analyzing Underlying Deterministic Models

Alexandre Chotard, Anne Auger

We consider Markov chains that obey the following general non-linear state space model: ${\Phi }_{k+1}=F({\Phi }_k,\alpha ({\Phi }_k,U_{k+1}))$ where the function $F$ is $C^1$ while $\alpha$ is typically d…