Integro-local theorems for sums of independent random vectors in the series scheme

Mathematical Notes

Volumn 79, Issue 3-4, 2006, Pages 468-482

  Borovkov, A A ^a   Mogul'skii, A A ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Independent identically distributed random vectors; Integro local theorems; Large deviations; Limit theorems; Summation theory; Weak convergence

Indexed keywords

EID: 33646004908     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11006-006-0053-3     Document Type: Article

References (12)

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4. L. A. Shepp, "A local limit theorem," Ann. Math. Statist., 35 (1964), 419-423.
5. C. J. Stone, "Local limit theorems for asymptotically stable distributions," Notices Amer. Math. Soc., 11 (1964), 465.
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8. A. A. Borovkov and A. A. Mogul'skii, Tear. Veroyatnost. i Primenen. [Theory Probab. Appl.], ibid, 45 (2000), no. 1, 5-19.
9. R. N. Bhattacharya and R. Ranga Rao, Normal Approximations and Asymptotic Expansions, Wiley, New York-London-Sydney, 1976; Russian translation: Nauka, Moscow, 1982.
10. V. V. Petrov, Sums of Independent Random Variables [in Russian], Nauka, Moscow, 1972.
11. W. Feller, An Introduction to Probability Theory, vol. II, 2nd ed., Wiley, New York-London-Sydney, 1971; Russian translation: vol. II, Mir, Moscow, 1967.
12. A. A. Borovkov, Probability Theory [in Russian], 3rd revised ed., Editorial URSS; Moscow, Izd-vo MI SB RAS, Novosibirsk, 1999.