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Asymptotic behavior of the stationary probabilities for two-dimensional positive random walks. (English. Russian original) Zbl 0307.60060
Sib. Math. J. 14, 109-118 (1973); translation from Sib. Mat. Zh. 14, 156-169 (1973).

MSC:
60G50 Sums of independent random variables; random walks
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References:
[1] V. A. Malyshev, ?An analytic method in theory of two-dimensional positive random walks,? Sibirsk. Matem. Zh.,13, No. 6, 1314-1329 (1972).
[2] J. W. Milnor, Morse Theory, Princeton University Press (1963).
[3] V. I. Arnol’d, ?Singularities of smooth mappings,? Usp. Matem. Nauk,23, No. 1, 3-44 (1968).
[4] M. A. Lavrent’ev and B. V. Shabat, Methods of Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1958).
[5] V. A. Malyshev, ?On the poles of rational generating functions. Probabilities of the appearance of combinations,? Litovskii Matem. Sbornik,5, No. 4, 585-591 (1965). · Zbl 0139.34703
[6] V. A. Malyshev, Random Walks. Wiener-Hopf Equations in a Quadrant. Galois Automorphisms [in Russian], Izd. Mosk. Un-ta, Moscow (1970).
[7] K. L. Chung, Homogeneous Markov Chains [Russian translation], Mir, Moscow (1965).
[8] A. A. Borovkov, ?New limit theorems in boundary-value problems for sums of independent random terms,? Sibirsk. Matem. Zh.,3, No. 5, 645-694 (1962).
[9] W. J. Pabjett and C. P. Tsokos, ?Existence of a stochastic integral equation in turbulence theory,? J. Math. Phys.,12, No. 2 (1971).
[10] R. N. Pederson, ?Laplace’s method for two parameters,? Pacif. J. Math.,15, No. 5, 585-596 (1965). · Zbl 0158.13102
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