Geodesic
Inequalities for transition probabilities with taboos and their applications
Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 451-488 Cet article a éte moissonné depuis la source Math-Net.Ru

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For geometrically ergodic Markov chains explicit estimates are obtained for the accuracy of approximation of transition probabilities with taboos $_Hp^{(t)}(x,B)$ by the variables $(1-\pi(H))^{t-1}\pi(B)$, where $\pi(\,\cdot\,)$ is a stationary distribution. These estimates are used for the proof of limit theorems on the distribution of the moment of first entry of the trajectory of a Markov chain into a given set and on the distribution of the number of states appearing in a segment of the trajectory of a Markov chain a given number of times. Bibliography: 24 titles. 
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A. M. Zubkov. Inequalities for transition probabilities with taboos and their applications. Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 451-488. http://geodesic.mathdoc.fr/item/SM_1980_37_4_a0/

[1] Chzhun Kai-lai, Odnorodnye tsepi Markova, izd-vo “Mir”, Moskva, 1964

[2] P. Mandl, “Ob asimptoticheskom povedenii veroyatnostei v gruppakh sostoyanii odnorodnoi tsepi Markova”, Čas. pro pěst. mat., 84:2 (1959), 140–149 | MR | Zbl

[3] J. N. Darroch, E. Seneta, “On quasi-stationary distributions in absorbing discrete finite Markov chains”, J. Appl. Probab., 2:1 (1965), 88–100 | DOI | MR | Zbl

[4] E. Seneta, D. Vere-Jones, “On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states”, J. Appl. Probab., 3:3 (1966), 403–434 | DOI | MR | Zbl

[5] R. L. Tweedie, “Quasi-stationary distributions for Markov chains on a general state space”, J. Appl. Probab., 11:4 (1974), 726–741 | DOI | MR | Zbl

[6] Dzh. L. Dub, Veroyatnostnye protsessy, IL, Moskva, 1956

[7] A. M. Zubkov, “Tsepi Markova, blizkie k posledovatelnosti nezavisimykh ispytanii”, Matem. zametki, 25:3 (1979), 465–474 | MR | Zbl

[8] M. Loev, Teoriya veroyatnostei, IL, Moskva, 1962 | MR

[9] G. Lorden, “On excess over the boundary”, Ann. Math. Statist., 41:2 (1970), 520–527 | DOI | MR | Zbl

[10] V. V. Kalashnikov, “Ravnomernaya otsenka skorosti skhodimosti v teoreme vosstanovleniya dlya diskretnogo vremeni”, Teoriya veroyatn., XXII:2 (1977), 399–403 | MR

[11] V. V. Kalashnikov, Kachestvennyi analiz povedeniya slozhnykh sistem metodom probnykh funktsii, izd-vo “Nauka”, Moskva, 1978 | MR

[12] N. N. Popov, “Usloviya geometricheskoi ergodichnosti dlya schetnykh tsepei Markova”, DAN SSSR, 234:2 (1977), 316–319 | MR | Zbl

[13] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 1, izd-vo “Mir”, Moskva, 1967

[14] B. A. Sevastyanov, “Predelnyi zakon Puassona v skheme summ zavisimykh sluchainykh velichin”, Teoriya veroyatn., XVII:4 (1972), 733–738

[15] V. F. Kolchin, B. A. Sevastyanov, V. P. Chistyakov, Sluchainye razmescheniya, izd-vo “Nauka”, Moskva, 1976 | MR

[16] A. S. Ambrosimov, “Normalnyi zakon v skheme summ zavisimykh sluchainykh velichin, rassmotrennykh B. A. Sevastyanovym”, Teoriya veroyatn., XXI:1 (1976), 184–189 | MR

[17] N. V. Smirnov, “O priblizhenii plotnostei raspredeleniya sluchainykh velichin”, Uchenye zapiski MGPI im. V. P. Potemkina, XVI:3 (1951), 69–96; см. также Н. В. Смирнов, “Теория вероятностей и математическая статистика”, Избранные труды, 1970, 205–223, изд-во “Наука”, Москва

[18] P. F. Belyaev, “O sovmestnom raspredelenii chastot iskhodov v tsepyakh Markova s bolshim chislom sostoyanii”, Teoriya veroyatn., XXII:3 (1977), 534–545

[19] V. P. Chistyakov, “Diskretnye predelnye raspredeleniya v zadache o drobinkakh s proizvolnymi veroyatnostyami popadaniya v yaschiki”, Matem. zametki, 1:1 (1967), 9–16 | MR | Zbl

[20] P. F. Belyaev, “O veroyatnosti nepoyavleniya zadannogo chisla iskhodov”, Teoriya veroyatn., IX:3 (1964), 541–547 | MR | Zbl

[21] P. F. Belyaev, “O veroyatnosti nepoyavleniya zadannogo chisla $s$-iskhodov v slozhnykh tsepyakh Markova”, Teoriya veroyatn., X:3 (1965), 547–551 | MR

[22] V. F. Kolchin, V. P. Chistyakov, “Predelnye raspredeleniya chisla nepoyavivshikhsya $s$-tsepochek v polinomialnoi skheme”, Teoriya veroyatn., XIX:4 (1974), 855–864

[23] A. M. Zubkov, V. G. Mikhailov, “O povtoreniyakh $s$-tsepochek v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatn., XXIV:2 (1979), 267–279 | MR

[24] A. S. Ambrosimov, “Ob asimptoticheskom povedenii maksimuma v odnorodnoi tsepi Markova s bolshim chislom iskhodov”, Teoriya veroyatn., XXIII:2 (1978), 438–445 | MR