On necessary and sufficient conditions for the convergence of the renewal density

On necessary and sufficient conditions for the convergence of the renewal density
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by Walter L. Smith PDF

Trans. Amer. Math. Soc. 104 (1962), 79-100 Request permission

References

David Blackwell, Extension of a renewal theorem, Pacific J. Math. 3 (1953), 315–320. MR 54880
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William Feller and S. Orey, A renewal theorem, J. Math. Mech. 10 (1961), 619–624. MR 0130721
B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR 0062975
Walter L. Smith, Asymptotic renewal theorems, Proc. Roy. Soc. Edinburgh Sect. A 64 (1954), 9–48. MR 60755
Walter L. Smith, Extensions of a renewal theorem, Proc. Cambridge Philos. Soc. 51 (1955), 629–638. MR 71660, DOI 10.1017/s030500410003070x

Contributions to Probability and Statistics

Walter L. Smith, On some general renewal theorems for nonidentically distributed variables, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 467–514. MR 0133890
Sven Täcklind, Fourieranalytische Behandlung vom Erneuerungsproblem, Skand. Aktuarietidskr. 28 (1945), 68–105 (German). MR 13838, DOI 10.1080/03461238.1945.10404920

Theory of fourier integrals