A review of asymptotic convergence for general state space Markov chains
نویسنده
چکیده
We review notions of small sets, φ-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions.
منابع مشابه
A review of asymptotic convergence forgeneral state space
We review notions of small sets,-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions.
متن کاملAsymptotic optimality of isoperimetric constants with respect to L(π)-spectral gaps
In this paper we investigate the existence of L(π)-spectral gaps for π-irreducible, positive recurrent Markov chains on general state space. We obtain necessary and sufficient conditions for the existence of L(π)spectral gaps in terms of a sequence of isoperimetric constants and establish their asymptotic behavior. It turns out that in some cases the spectral gap can be understood in terms of c...
متن کاملThe Rate of Rényi Entropy for Irreducible Markov Chains
In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.
متن کاملRelative Entropy Rate between a Markov Chain and Its Corresponding Hidden Markov Chain
In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...
متن کاملConvergence results for the (1, )-SA-ES using the theory of -irreducible Markov chains
This paper investigates theoretically the (1, )-SA-ES on the well known sphere function. We prove sufficient conditions on the parameters of the algorithm ensuring the convergence of 1/n ln(||Xn||), where Xn is the parent at generation n. This in turn guarantees the asymptotic log-linear convergence or divergence of the algorithm. The technique used for this analysis calls upon the theory of Ma...
متن کامل