Volume : 12, Issue : 1, JAN 2026
PARTIAL ATTRACTION, SEMI-STABLE LAWS, AND ITERATED LOGARITHM RESULTS: A SURVEY
GOOTY DIVANJI, KABELO MOSEKI
Abstract
The work surveys stable, semi-stable, and infinitely divisible laws, emphasizing domains of attraction and partial attraction. It highlights key results on limit theorems, especially laws of the iterated logarithm under power normalisation. Contributions include extensions to stable and semi-stable domains, subsequences, delayed sums, random sums, and related stochastic processes.
Keywords
STABLE, SEMI-STABLE, INFINITELY DIVISIBLE LAWS AND DOMAIN OF PARTIAL ATTRACTION.
Article : Download PDF
Cite This Article
IESRJ
International Educational Scientific Research Journal
E-ISSN: 2455-295X
International Indexed Journal | Multi-Disciplinary Refereed Research Journal
ISSN: 2455-295X
Peer-Reviewed Journal - Equivalent to UGC Approved Journal
Peer-Reviewed Journal
Article No : 2
Number of Downloads : 40
References
1. Allan Gut (1986): Law of Iterated Logarithm for Sub sequences, Probab. Math. Statist. 7(1),27–58.
2. Bingham, N. H. (1986): Variants on the Law of the Iterated Logarithm, Bull. London Math. Soc. 18, 433–467.
3. Divanji, G. and Vasudeva, R. (1989): Tail Behavior of Distributions in the Domain of Partial Attraction and Some Related Iterated Logarithm Laws, Sankhy? Ser. A 51(2), 196–204.
4. Divanji, G. (1998): Almost Sure Limit Points for Sub sequences of Partial Sums, presented at the IV Conference of the Society for Development of Statistics, Hyderabad, 14-11-98.
5. Divanji, G. and Vasudeva, R. (2002): Law of Iterated Logarithm — Cluster Points for Sub sequences of Bivariate Summands, communicated to Stochastic Modelling and Applications.
6. Feller, W. (1986): An Introduction to Probability Theory and Its Applications, Vol. II, Fourth Wiley Eastern Reprint.
7. Gnedenko, B. V. and Kolmogorov, A. N. (1954): Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA.
8. Ingrid Tarring (1987): Law of the Iterated Logarithm — Cluster Points of Deterministic and Random Sub sequences, Prob. Math. Statist. 8, 133–141.
9. Kruglov, V. M. (1972): On the Extension of the Class of Stable Distributions, Theory Probab. Appl. 17, 685–694.
10. Lepage, R. D. (1972): Log–Log Law for Gaussian Processes, Z Wahrscheinlichkeitstheorieverw. Geb. 25, 103–108.
11. Pakshirajan, R. P. and Vasudeva, R. (1977): A Law of the Iterated Logarithm for Stable Summands, Trans. Amer. Math. Soc. 232, 33–42.
12. Stout, W. (1974): Almost Sure Convergence, Academic Press.
13. Vasudeva, R. and Divanji, G. (1991): Law of Iterated Logarithm for Random Subsequences, Statistics and Probability Letters 12, 189–194.
14. Vasudeva, R. and Savitha, S. (1993): On the Increments of the Wiener Process — A Look Through Sub sequences, Stochastic Processes and their Applications 47, 153–158.
