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The Martin boundary for random walk. (English) Zbl 0141.15601

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[1] D. R. Cox and Walter L. Smith, A direct proof of a fundamental theorem of renewal theory, Skand. Aktuarietidskr. 36 (1953), 139 – 150. · Zbl 0053.26801
[2] J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech. 8 (1959), 433 – 458; erratum 993. · Zbl 0101.11503
[3] J. L. Doob, J. L. Snell, and R. E. Williamson, Application of boundary theory to sums of independent random variables., Contributions to probability and statistics, Stanford Univ. Press, Stanford, Calif., 1960, pp. 182 – 197. · Zbl 0094.32202
[4] B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. · Zbl 0056.36001
[5] Paul-Louis Hennequin, Processus de Markoff en cascade, Ann. Inst. H. PoincarĂ© 18 (1963), 109 – 195 (1963) (French). · Zbl 0141.15802
[6] G. A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math. 4 (1960), 313 – 340. · Zbl 0094.32103
[7] Walter L. Smith, A frequency-function form of the central limit theorem, Proc. Cambridge Philos. Soc. 49 (1953), 462 – 472. · Zbl 0053.09603
[8] Frank Spitzer, Principles of random walk, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. · Zbl 0979.60002
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