Geodesic
Local limit theorems for conditionally independent random variables controlled by a finite Markov chain
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 143-148

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The sufficient conditions for the validity of local theorems for conditionally independent random variables controlled by a finite homogeneous regular Markov chain are given in terms of conditional distributions of summands.
Keywords: conditionally independent random variables, local theorems for densities, local theorem for lattice distributions, normal attraction to the stable law. 
T. Shervashidze. Local limit theorems for conditionally independent random variables controlled by a finite Markov chain. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 143-148. http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a14/
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     author = {T. Shervashidze},
     title = {Local limit theorems for conditionally independent random variables controlled by a finite {Markov} chain},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {143--148},
     year = {1999},
     volume = {44},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a14/}
}
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