Limit theorems for weighted sums of infinite variance random variables attracted to integrals of linear fractional stable motions

Tokyo Journal of Mathematics

Volumn 31, Issue 2, 2008, Pages 259-271

  Maejima, Makoto ^a   Suzuki, Sakurako ^b  

^a KEIO UNIVERSITY   (Japan)

^b OCHANOMIZU UNIVERSITY   (Japan)

Author keywords

Integral with respect to linear fractional stable motion; Linear fractional stable motion; Slowly varying function; Weighted sum

Indexed keywords

EID: 77955730556     PISSN: 03873870     EISSN: None     Source Type: Journal    
DOI: 10.3836/tjm/1233844051     Document Type: Article

References (7)

1. AVRAM, F. and TAQQU, M. S., Weak convergence of moving averages with infinite variance, in EBERLEIN, E. and TAQQU, M. S. (eds.), Dependence in Probability and Statistics, Birkauser, Boston, 399–415 (1986).
2. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L., Regular Variation, New York, Cambridge Univ. Press, 1987.
3. IRISAWA, M., MAEJIMA, M. and SHIMOMURA, S., A limit theorem for weighted sums of infinite variance random variables with long-range dependence, KSTS/RR-03/005, Dept. of Math., Keio Univ., 2003.
4. KASAHARA, Y. and MAEJIMA, M., Weighted sums of i.i.d. random variables attracted to integrals of stable processes, Probab. Th. Rel. Fields 78, 75–96 (1988).
5. MAEJIMA, M., A self-similar process with nowhere bounded sample paths, Z. Wahrscheinlichkeitstheorie verw. Gebiete 65, 115–119 (1983).
6. PIPIRAS, V. and TAQQU, M. S., Convergence of weighted sums of random variables with long-range dependence, Stoch. Proc. Appl. 90, 157–174 (2000).
7. SAMORODNITSKY, G. and TAQQU, M. S., Stable Non-Gaussian Processes, London, Chapman and Hall, 1994.