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On characteristic functions and renewal theory. (English) Zbl 0133.40504

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[1] David Blackwell, A renewal theorem, Duke Math. J. 15 (1948), 145 – 150. · Zbl 0030.20102
[2] David Blackwell, Extension of a renewal theorem, Pacific J. Math. 3 (1953), 315 – 320. · Zbl 0052.14104
[3] Kai Lai Chung and Harry Pollard, An extension of renewal theory, Proc. Amer. Math. Soc. 3 (1952), 303 – 309. · Zbl 0047.12403
[4] K. L. Chung and J. Wolfowitz, On a limit theorem in renewal theory, Ann. of Math. (2) 55 (1952), 1 – 6. · Zbl 0047.12402 · doi:10.2307/1969414 · doi.org
[5] P. Erdös, W. Feller, and H. Pollard, A property of power series with positive coefficients, Bull. Amer. Math. Soc. 55 (1949), 201 – 204. · Zbl 0032.27802
[6] Carl-Gustav Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math. 77 (1945), 1 – 125. · Zbl 0060.28705 · doi:10.1007/BF02392223 · doi.org
[7] William Feller, Fluctuation theory of recurrent events, Trans. Amer. Math. Soc. 67 (1949), 98 – 119. · Zbl 0039.13301
[8] William Feller and S. Orey, A renewal theorem, J. Math. Mech. 10 (1961), 619 – 624. · Zbl 0096.33401
[9] A. O. Gel\(^{\prime}\)fond, An estimate for the remainder term in the limit theorem for recurrent events, Teor. Verojatnost. i Primenen. 9 (1964), 327 – 331 (Russian, with English summary).
[10] Samuel Karlin, On the renewal equation, Pacific J. Math. 5 (1955), 229 – 257. · Zbl 0067.34902
[11] A. N. Kolmogorov, Markov chains with a countable number of possible states, Bull. Moscow Univ. Ser. A 1 (1937), 1-16.
[12] Walter L. Smith, Asymptotic renewal theorems, Proc. Roy. Soc. Edinburgh. Sect. A. 64 (1954), 9 – 48. · Zbl 0055.12402
[13] Walter L. Smith, Infinitesimal renewal processes, Contributions to probability and statistics, Stanford Univ. Press, Stanford, Calif., 1960, pp. 396 – 413. · Zbl 0095.32702
[14] Charles Stone, A local limit theorem for nonlattice multi-dimensional distribution functions, Ann. Math. Statist. 36 (1965), 546 – 551. · Zbl 0135.19204 · doi:10.1214/aoms/1177700165 · doi.org
[15] Sven Täcklind, Fourieranalytische Behandlung vom Erneuerungsproblem, Skand. Aktuarietidskr. 28 (1945), 68 – 105 (German). · Zbl 0063.07274
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