Geodesic
On the Convergence Rate in a Local Renewal Theorem for a Random Markov Walk
Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 521-532 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose that a sequence $\{X_n\}_{n\ge 0}$ of random variables is a homogeneous indecomposable Markov chain with finite set of states. Let $\xi_n$, $n\in\mathbb{N}$, be random variables defined on the chain transitions. The reconstruction function $$ u_k:=\sum_{n=0}^{+\infty} \mathsf P(S_n=k), \qquad k\in\mathbb{N}, $$ where $S_0:=0$ and $S_n:=\xi_1+\dots + \xi_n$, $n\in\mathbb{N}$, is introduced. It is shown that this function converges to its limit with exponential rate, and an explicit description of the exponent is given.
Keywords: local reconstruction theorem
Mots-clés : Markov chain. 
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G. A. Bakai. On the Convergence Rate in a Local Renewal Theorem for a Random Markov Walk. Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 521-532. http://geodesic.mathdoc.fr/item/MZM_2024_115_4_a3/

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