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Volumn 151, Issue 1, 1970, Pages 263-291

Strong renewal theorems with infinite mean

Author keywords

Characteristic function; Convolution; Domain of attraction; Infinite mean; Inversion formulas; Karamata Tauberian theorem; Local limit theorems; Nonarithmetic; Probability distributions; Regular and slow variation; Renewal function; Renewal process; Strong renewal theorem; Waiting times; Weak convergence of measures

Indexed keywords


EID: 84963874608     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1970-0268976-9     Document Type: Article
Times cited : (106)

References (13)
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    • E. B. Dynkin, Some limit theorems for sums of independent random variables with infinite mathematical expectations, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 247-266
    • (1955) Izv. Akad. Nauk SSSR Ser. Mat , vol.19 , pp. 247-266
    • Dynkin, E.B.1
  • 6
    • 22144438077 scopus 로고
    • A renewal theorem
    • W. Feller and S. Orey, A renewal theorem, J. Math. Mech. 10 (1961), 619-624.
    • (1961) J. Math. Mech , vol.10 , pp. 619-624
    • Feller, W.1    Orey, S.2
  • 7
    • 51649220070 scopus 로고
    • A discrete renewal theorem with infinite mean
    • A. Garsia and J. Lamperti, A discrete renewal theorem with infinite mean, Comment. Math. Helv. 37 (1962/63), 221-234.
    • (1962) Comment. Math. Helv. , vol.37 , pp. 221-234
    • Garsia, A.1    Lamperti, J.2
  • 8
    • 0002379945 scopus 로고
    • Notes on Fourier series. Ill: Asymptotic formulae for the sums of certain trigonometrical series
    • G. H. Hardy and W. W. Rogosinski, Notes on Fourier series. Ill: Asymptotic formulae for the sums of certain trigonometrical series, Quart. J. Math. Oxford Ser. 16 (1945), 49-58.
    • (1945) Quart. J. Math. Oxford Ser , vol.16 , pp. 49-58
    • Hardy, G.H.1    Rogosinski, W.W.2
  • 9
    • 0008390912 scopus 로고
    • Some limit theorems for stochastic processes
    • J. Lamperti, Some limit theorems for stochastic processes, J. Math. Mech. 7 (1958), 433-448.
    • (1958) J. Math. Mech , vol.7 , pp. 433-448
    • Lamperti, J.1
  • 11
    • 0000983367 scopus 로고
    • A local limit theorem for nonlattice multi-dimensional distribution functions
    • C. J. Stone, A local limit theorem for nonlattice multi-dimensional distribution functions, Ann. Math. Statist. 36 (1965), 546-551.
    • (1965) Ann. Math. Statist , vol.36 , pp. 546-551
    • Stone, C.J.1
  • 12
    • 0000423678 scopus 로고
    • Renewal theorems when the first or the second moment is infinite
    • J. L. Teugels, Renewal theorems when the first or the second moment is infinite, Ann. Math. Statist. 39 (1968), 1210-1219.
    • (1968) Ann. Math. Statist , vol.39 , pp. 1210-1219
    • Teugels, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.