Strong law of large numbers for Markov chains field on a Bethe tree
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Publication:1582655
DOI10.1016/S0167-7152(00)00053-5zbMath0981.60064OpenAlexW2074342432WikidataQ126843269 ScholiaQ126843269MaRDI QIDQ1582655
Publication date: 15 October 2000
Published in: Statistics \& Probability Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0167-7152(00)00053-5
Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)
Related Items (24)
THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT ⋮ A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT ⋮ The Shannon–McMillan theorem for Markov chains in Markovian environments indexed by homogeneous trees ⋮ The strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment ⋮ Limit theorems for asymptotic circular mth-order Markov chains indexed by an m-rooted homogeneous tree ⋮ Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree ⋮ A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree ⋮ A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment ⋮ New gaps between zeros of fourth-order differential equations via Opial inequalities ⋮ The generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree ⋮ THE GENERALIZED ENTROPY ERGODIC THEOREM FOR NONHOMOGENEOUS MARKOV CHAINS INDEXED BY A HOMOGENEOUS TREE ⋮ Strong law of large numbers of the offspring empirical measure for Markov chains indexed by homogeneous tree ⋮ Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree ⋮ Strong laws of large numbers for the mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree ⋮ Some limit properties of the harmonic mean of transition probabilities for Markov chains in Markovian environments indexed by Cayley's trees ⋮ Some limit properties for Markov chains indexed by a homogeneous tree. ⋮ A limit theorem for partial sums of random variables and its applications. ⋮ Unnamed Item ⋮ Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree ⋮ Some limit properties of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree ⋮ Some limit properties for the \(m\)th-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree ⋮ The strong law of large numbers and the Shannon-McMillan theorem for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree ⋮ Strong laws of large numbers and the asymptotic equipartition property for the asymptotic \(N\)-branch Markov chains indexed by a Cayley tree ⋮ The asymptotic behavior for Markov chains in a finite i.i.d random environment indexed by cayley trees
Cites Work
- Unnamed Item
- Markov random fields on an infinite tree
- Markov chains indexed by trees
- A limit theorem for the entropy density of nonhomogeneous Markov information source
- An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
- Entropic aspects of random fields on trees
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