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References
Basu, A.K.: Invariance theorems for first passage time random variables. Canad. Math. Bull. Vol. 15, 171–176 (1972)
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Blackwell, D.: Extension of a renewal theorem. Pacific J. Math. 3, 315–320 (1953)
Doob, J.L.: Renewal theory from the point of view of the theory of probability. Trans. Amer. Math. Soc. 63, 422–438 (1948)
Gut, A.: On the moments and limit distributions of some first passage times. Techn. Report 43, Dept. Math., Univ. of Uppsala, Sweden (1972). Annals of Probability (to appear 1974)
Heyde, C.C.: Some renewal theorems with application to a first passage problem. Ann. Math. Statist. 37, 699–710 (1966)
Heyde, C.C.: Asymptotic renewal results for a natural generalization of classical renewal theory. J. Roy. Statist. Soc., Ser. B 29, 141–150 (1967)
Richter, W.: Limit theorems for sequences of random variables with sequences of random indices. Theor. Probab. Appl. X, 74–84 (1965)
Siegmund, D.O.: Some one-sided stopping rules. Ann. Math. Statist. 38, 1641–1646 (1967)
Siegmund, D.O.: On the asymptotic normality of one-sided stopping rules. Ann. Math. Statist. 39, 1493–1497 (1968)
Vervaat, W.: Functional central limit theorems for processes with positive drift and their inverses. Z. Wahrscheinlichkeitstheorie verw. Gebiete 23, 245–253 (1972)
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Gut, A. A functional central limit theorem connected with extended renewal theory. Z. Wahrscheinlichkeitstheorie verw Gebiete 27, 123–129 (1973). https://doi.org/10.1007/BF00536623
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DOI: https://doi.org/10.1007/BF00536623