Geodesic
Factorization methods and boundary problems for sums of random
Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 815-852

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This work concerns asymptotic study of the joint distribution of the maximum of a sequence of sums and the sums themselves on finite regular Markov chains. To this end, a series of lemmas are demonstrated on factorization of elements of general algebraic rings, as well as factorization identities having interest in themselves which provide a connection between various distributions pertaining to the random processes in question. 
@article{IM2_1969_3_4_a6,
     author = {E. L. Presman},
     title = {Factorization methods and boundary problems for sums of random},
     journal = {Izvestiya. Mathematics },
     pages = {815--852},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a6/}
}
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E. L. Presman. Factorization methods and boundary problems for sums of random. Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 815-852. http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a6/