×

zbMATH — the first resource for mathematics

Ratio theorems for random walks. I. (English) Zbl 0121.35201

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kai Cai Chung, Markov chains with stationary transition probabilities, Berlin, 1960. · Zbl 0092.34304
[2] K. L. Chung and P. Erdös, Probability limit theorems assuming only the first moment I,Memoir n o 6, Amer. Math. Soc., 1951. · Zbl 0042.37601
[3] K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variables.Memori n o 6, Amer. Math. Soc., 1951. · Zbl 0042.37502
[4] D. A. Darling and M. Kac, On occupation times for Markoff processes,Trans. Amer. Math. Soc. 84 (1957), pp. 444–458. · Zbl 0078.32005 · doi:10.1090/S0002-9947-1957-0084222-7
[5] Gustav Doetsch, Handbuch der Laplace-Transformation, Band I, Basel 1950. · Zbl 0040.05901
[6] William Feller, An introduction to probability theory and its applications, vol I 2nd ed., New York, N. Y., 1957. · Zbl 0077.12201
[7] G. A. Hunt, Some theorems concerning Brownian motion,Trans. Amer. Math. Soc. 81 (1956), pp. 294–319. · Zbl 0070.36601 · doi:10.1090/S0002-9947-1956-0079377-3
[8] M. Kac, A class of limit theorems,Trans. Amer. Math. Soc. 84 (1957), pp. 459–471. · Zbl 0078.31503 · doi:10.1090/S0002-9947-1957-0086435-7
[9] H. Kesten, D. Ornstein and F. Spitzer, A general property or random walk,Bull. Amer. Math. Soc. 68 (1962) pp. 526–528. · Zbl 0111.32701 · doi:10.1090/S0002-9904-1962-10808-8
[10] Paul Lévy, Théorie de l’addition des variables aléatoires, 2ième ed. Paris, 1954.
[11] Michel Loève, Probability theory, 3rd ed., Princeton, N. J., 1963.
[12] Frank Spitzer, A combinatorial lemma and its applications to probability theoryTrans. Amer. Math. Soc. 82, (1956) pp. 323–339. · Zbl 0071.13003 · doi:10.1090/S0002-9947-1956-0079851-X
[13] Frank Spitzer, Some properties of recurrent random walk,Ill. J. Math. 5 (1961) pp. 234–245. · Zbl 0109.36201
[14] Frank Spitzer, Hitting probabilities,J. of Math. and Mech. 11 (1962) pp. 593–614. · Zbl 0218.60061
[15] Frank Spitzer, Principles of random walk, to appear.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.