×

zbMATH — the first resource for mathematics

A Tauberian theorem and its probability interpretation. (English) Zbl 0216.21201

MSC:
60G50 Sums of independent random variables; random walks
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Erik Sparre Andersen, On the fluctuations of sums of random variables. II, Math. Scand. 2 (1954), 195 – 223. · Zbl 0058.12102
[2] Glen Baxter, An operator identity, Pacific J. Math. 8 (1958), 649 – 663. · Zbl 0088.11201
[3] David Blackwell, Extension of a renewal theorem, Pacific J. Math. 3 (1953), 315 – 320. · Zbl 0052.14104
[4] K. L. Chung and P. Erdös, Probability limit theorems assuming only the first moment. I, Mem. Amer. Math. Soc., No. 6 (1951), 19. · Zbl 0042.37601
[5] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0053.26802
[6] W. Feller, An introduction to probability theory and its applications, vol. 1, New York, 1950. · Zbl 0039.13201
[7] T. E. Harris, The existence of stationary measures for certain Markov processes, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954 – 1955, vol. II, University of California Press, Berkeley and Los Angeles, 1956, pp. 113 – 124.
[8] Félix Pollaczek, Fonctions caractéristiques de certaines répartitions définies au moyen de la notion d’ordre. Application à la théorie des attentes, C. R. Acad. Sci. Paris 234 (1952), 2334 – 2336 (French). · Zbl 0047.37303
[9] Frank Spitzer, A combinatorial lemma and its application to probability theory, Trans. Amer. Math. Soc. 82 (1956), 323 – 339. · Zbl 0071.13003
[10] Frank Spitzer, The Wiener-Hopf equation whose kernel is a probability density, Duke Math. J. 24 (1957), 327 – 343. · Zbl 0082.32003
[11] F. Spitzer and C. Stone, Some applications of Toeplitz matrices to probability theory (to appear in Illinois J. Math.). · Zbl 0124.34403
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.