Geodesic
Large-Deviation Probabilities for One-Dimensional Markov Chains. Part~3: Prestationary Distributions in the Subexponential Case
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 640-657

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This paper continues investigations of A. A. Borovkov and D. A. Korshunov [Theory Probab. Appl., 41 (1996), pp. 1–24 and 45 (2000), pp. 379–405]. We consider a time-homogeneous Markov chain $\{X(n)\}$ that takes values on the real line and has increments which do not possess exponential moments. The asymptotic behavior of the probability ${\mathbf P}\{X(n)\ge x\}$ is studied as $x\to\infty$ for fixed values of time $n$ and for unboundedly growing $n$ as well.
Mots-clés : Markov chain
Keywords: asymptotic behavior of large-deviation probabilities, subexponential distribution, invariant measure, integrated distribution tail. 
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     author = {A. A. Borovkov and D. A. Korshunov},
     title = {Large-Deviation {Probabilities} for {One-Dimensional} {Markov} {Chains.} {Part~3:} {Prestationary} {Distributions} in the {Subexponential} {Case}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {640--657},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a1/}
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A. A. Borovkov; D. A. Korshunov. Large-Deviation Probabilities for One-Dimensional Markov Chains. Part~3: Prestationary Distributions in the Subexponential Case. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 640-657. http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a1/