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Transactions of the American Mathematical Society

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On characteristic functions and renewal theory


Author: Charles Stone
Journal: Trans. Amer. Math. Soc. 120 (1965), 327-342
MSC: Primary 60.70
DOI: https://doi.org/10.1090/S0002-9947-1965-0189151-0
MathSciNet review: 0189151
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  • [1] D. H. Blackwell, A renewal theorem, Duke Math. J. 15 (1948), 145-150. MR 0024093 (9:452a)
  • [2] -, Extension of a renewal theorem, Pacific J. Math. 3 (1953), 315-320. MR 0054880 (14:994c)
  • [3] K. L. Chung and H. Pollard, An extension of renewal theory, Proc. Amer. Math. Soc. 3 (1952), 303-309. MR 0048734 (14:61d)
  • [4] K. L. Chung and J. Wolfowitz, On a limit theorem in renewal theory, Ann. of Math. (2) 55 (1952), 1-6. MR 0044769 (13:475e)
  • [5] P. Erdös, W. Feller and H. Pollard, A property of power series with positive coefficients, Bull. Amer. Math. Soc. 55 (1949), 201-204. MR 0027867 (10:367d)
  • [6] C. G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta. Math. 77 (1945), 1-125. MR 0014626 (7:312a)
  • [7] W. Feller, Fluctuation theory of recurrent events, Trans. Amer. Math. Soc. 67 (1949), 98-119. MR 0032114 (11:255c)
  • [8] W. Feller and S. Orey, A renewal theorem, J. Math. Mech. 10 (1961), 619-624. MR 0130721 (24:A581)
  • [9] A. O. Gelfond, An estimate of the remainder term in a limit theorem for recurrent events, Theor. Probability Appl. 9 (1964), 327-331. (Russian) MR 0163373 (29:676)
  • [10] S. Karlin, On the renewal equation, Pacific J. Math. 5 (1955), 229-257. MR 0070877 (17:49b)
  • [11] A. N. Kolmogorov, Markov chains with a countable number of possible states, Bull. Moscow Univ. Ser. A 1 (1937), 1-16.
  • [12] W. L. Smith, Asymptotic renewal theorems, Proc. Roy. Soc. Edinburgh Sect. A. 64 (1954), 9-48. MR 0060755 (15:722f)
  • [13] -, Infinitesimal renewal processes, Contribution to Prob. and Stat., Stanford Univ. Press, Stanford, Calif., 1960; pp. 396-413. MR 0120670 (22:11419)
  • [14] C. J. Stone, A local limit theorem for nonlattice multidimensional distribution functions, Ann. Math. Statist. 36 (1965), 546-551. MR 0175166 (30:5351)
  • [15] S. Täcklind, Fourieranalytische Behandlung vom Erneuerungsproblem, Skand. Aktuarietidskr. 28 (1945), 68-105. MR 0013838 (7:207b)

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DOI: https://doi.org/10.1090/S0002-9947-1965-0189151-0
Article copyright: © Copyright 1965 American Mathematical Society

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