Integro-local and integral limit theorems on the large deviations of sums of random vectors: Regular distributions

Siberian Mathematical Journal

Volumn 43, Issue 3, 2002, Pages 402-417

  Borovkov, A A ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Integral theorem; Integro local theorem; Large deviation; Sum of random vectors

Indexed keywords

EID: 0036258403     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015499132102     Document Type: Article

References (7)

1. Borovkov A. A. and Mogul'skiǐ A. A., "Integro-local limit theorems including large deviations for sums of random vectors. I, II," Teor. Veroyatnost. i Primenen., I: 43, No. 1, 3-17 (1998); II: 45, No. 1, 5-29 (2000).
2. Borovkov A. A. and Mogul'skiǐ A. A., "Integro-local limit theorems including large deviations for sums of random vectors. I, II," Teor. Veroyatnost. i Primenen., 1: 43, No. 1, 3-17 (1998); II: 45, No. 1, 5-29 (2000).
3. Borovkov A. A. and Borovkov K. A., "On large deviation probabilities for random walks. I: Regularly varying distribution tails," Teor. Veroyatnost. i Primenen., 46, No. 2, 209-232 (2001).
4. Borovkov A. A., "Estimates for the distribution of sums and maxima of sums of random variables without the Cramer condition," Sibirsk. Mat. Zh., 41, No. 5, 997-1038 (2000).
5. Borovkov A. A., Probability [in Russian], Èditorial URSS; Izdat. Sobolev Inst. Mat., Moscow; Novosibirsk (1999).
6. Petrov V. V., Limit Theorems for Sums of Independent Random Variables [in Russian], Nauka, Moscow (1987).
7. Pinelis I. F., "The problem of large deviations in the space of trajectories," Teor. Veroyatnost. i Primenen., 26, No. 1, 73-87 (1981).