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Original Articles

Moment Convergence of Reciprocals of some First Passage Times

Pages 135-146 | Published online: 14 Aug 2013

  • ChowY.S., HsiungC.A. and LaiT.A. (1979). Extended renewal theory and moment convergence in Anscombe's theorem. Ann. Probability 7, 304–318.
  • ChowY.S. and LaiT.L. (1978). Paley-type inequalities and convergence rates related to the law of large numbers and extended renewal theory. Z. Wahrsch. verw. Gebiete 45, 1–19.
  • ChowY.S. and LaiT.L. (1979). Moments of ladder variables for driftless random walks. Z. Wahrsch. verw. Gebiete 48, 253–257.
  • ChowY.S. and TeicherH. (1978). Probability Theory. Springer-Verlag, New York.
  • ErdösP. and KacM. (1946). On certain limit theorems of the theory of probability. Buli. Amer. Math. Soc. 52, 292–302.
  • FellerW. (1949). Fluctuation theory of recurrent events. Trans. Amer. Math. Soc. 67, 98–119.
  • GutA. (1974). On moments and limit distributions of some first passage times. Ann. Probability 2, 277–308.
  • HeydeC.C. (1966). Some renewal theorems with applications to a first passage problem. Ann. Math. Statist. 37, 699–710.
  • HeydeC.C. (1967). Asymptotic renewal results for a natural generalization of classical renewal theory. J. Roy. Statist. Soc. Ser. B. 29, 141–150.
  • LaiT.L. (1975). On uniform integrability in renewal theory. Bull. Inst. Math. Acad. Sinica 3, 99–105.
  • LaiT.L. (1976). Asymptotic moments of random walks with applications of ladder variables and renewal theory. Ann. Probability 4, 51–66.
  • MartinsekA. (1983). Sequential estimation with squared relative error loss. Bull. Inst. Math. Academia Sinica 11, 607–624.
  • McCabeB.J. and SheppL.A. (1970). On the supermum of Sn/n. Ann. Math. Statist. 41, 2166–2168.
  • SiegmundD. (1967). Some one-sided stopping unless. Ann. Math. Statist. 38, 164–1646.
  • SiegmundD. (1969). The variance of one-sided stopping rules. Ann. Math. Statist. 40, 1074–1077.
  • SmithW.L. (1954). Asymptotic renewal theorems. Proc. Roy Soc. Edinburgh Sect. A. 64, 9–48.
  • WoodroofeM. (1976). A renewal theorem for curved boundaries and moments of first passage times. Ann. Probability 4, 67–80.

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