On the Ergodicity of Certain Markov Chains in Random Environments
On the Ergodicity of Certain Markov Chains in Random Environments
Abstract We study the ergodic behaviour of a discrete-time process X which is a Markov chain in a stationary random environment. The laws of $$X_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>X</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math> are shown to converge to a limiting law in (weighted) total variation distance as $$t\rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math> . Convergence speed is …