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We describe estimators $chi_n(X_0,X_1,...,X_n)$, which when applied to an unknown stationary process taking values from a countable alphabet ${cal X}$, converge almost surely to $k$ in case the process is a $k$-th order Markov chain and to infinity otherwise.
We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of
Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There is, however, a very peculiar kind of discrete
We review recent results on the metastable behavior of continuous-time Markov chains derived through the characterization of Markov chains as unique solutions of martingale problems.
We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations
Let ${X_n}_{n=0}^{infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0le ile n$ in a strongly consistent way. Bailey and Ryabko