One-sided local large deviation and renewal theorems in the case of infinite mean

Probability Theory and Related Fields

Volumn 107, Issue 4, 1997, Pages 451-465

  Doney, R A ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031116513     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050093     Document Type: Article

References (11)

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4. Doney, R.A.: One-sided large deviation theorems in the case of infinite mean, Research report, Manchester Centre for Statistical Science 1995
5. Erickson, K.B.: Strong renewal theorems with infinite mean. Trans. Amer. Math. Soc. 151, 263-291 (1970)
6. Garsia, A., Lamperti, J.: A discrete renewal theorem with infinite mean. Comm. Math. Helv. 37, 221-234 (1963)
7. Nagaev, S.V.: Large deviations of sums of independent random variables. Ann. Probab. 7, 745-789 (1979)
8. Nagaev, S.V.: On the asymptotic behaviour of one-sided large deviation probabilities. Theory Probab. Appl. 26, 362-366 (1982)
9. Petrov, V.V.: Sums of Independent Random Variables. Berlin Heidelberg New York: Springer 1975
10. Tkachuk, S.G.: Limit theorems for sums of independent random variables belonging to the domain of attraction of a stable law. Candidate's dissertation, Tashent 1977 (in Russian)
11. Williamson, J.A.: Random walks and Riesz kernels. Pacific J Math. 25, 393-415 (1968)