A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors

Monatshefte fur Mathematik

Volumn 130, Issue 4, 2000, Pages 329-347

  Scheffler, Hans Peter ^a   Becker Kern, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Generalized domains of semistable attraction; Law of the iterated logarithm; Operator semistable laws; Randomly stopped sums; Regularly varying measures

Indexed keywords

EID: 0034359635     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050070031     Document Type: Article

References (30)

1. Araujo A, Giné E (1980) The Central Limit Theorem for Real and Banach Valued Random Variables. New York: Wiley
2. Becker-Kern P (1999) Stabile Randomisierte Grenzwertsätze. Dissertation, Universität Dortmund
3. Blum JR, Hanson DL, Rosenblatt JI (1962) On the central limit theorem for the sum of a random number of independent random variables. Z Wahrscheinlichkeitstheorie verw Geb 1: 389-393
4. Breiman L (1968) Probability. Reading, Mass: Addison-Wesley
5. d. Theory Probab Appl 57: 703-705
6. Chover J (1966) A law of the iterated logarithm for stable summands. Proc Amer Math Soc 17: 441-443
7. Chow YS, Teicher H, Wei CZ, Yu KF (1981) Iterated logarithm laws with random subsequences. Z Wahrscheinlichkeitstheorie verw Geb 57: 235-251
8. Curtis C (1974) Linear Algebra 3rd edn. Boston: Allyn and Bacon
9. th USSR-Japan Symposium on probability theory and mathematical statistics. Lect Notes Math. 1021: 167-176
10. Gut A (1991) Anscombe laws of the iterated logarithm. Prob Math Stat 12: 127-137
11. Hazod W (1999) Some new limit theorems for vector space and group-valued random variables. J Math Sci 93: 531-542
12. Hudson WN. Veeh HA, Weiner DC (1988) Moments of distributions attracted to operator stable laws. J Multivariate Anal 24: 1-10
13. N. Studia Math 61: 29-39
14. k. Proc Amer Math Soc 102: 341-348
15. Meerschaert MM, Scheffler HP (1996) Generalized domains of semistable attraction of nonnormal laws. J Applied Analysis 2: 203-215
16. Meerschaert MM, Scheffler HP (1997) The structure of generalized domains of semistable attraction. Stat Probab Letters 33: 367-372
17. Meerschaert MM, Scheffler HP (1997) Spectral decomposition for generalized domains of semistable attraction. J Theoretical Probab 10: 51-71
18. Meerschaert MM, Scheffler HP (1999) Multivariable regular variation of functions and measures. J Applied Analysis 5: 125-146
19. Mogyoródi J (1962) A central limit theorem for the sum of a random number of independent random variables. Publ Math Inst Hungar Acad Sci Ser A 7: 409-424
20. Rényi A (1970) Probability Theory. Amsterdam: North-Holland
21. Scheffler HP (1995) Moments of measures attracted to operator semi-stable laws. Stat Probab Letters 24: 187-192
22. Scheffler HP (2000) Multivariate R-O varying measures. Part I: Uniform bounds. Proc London Math Soc (to appear)
23. Scheffler HP (1999) Multivariate R-O varying measures. Part II: Individual bounds (submitted)
24. Scheffler HP (1999) Norming operators for generalized domains of semistable attraction (submitted)
25. Scheffler HP (2000) A law of the iterated logarithm for heavy tailed random vectors. Probab Theory Related Fields 116: 257-271
26. Sharpe M (1969) Operator-stable probability distributions on vector groups. Trans Amer Math Soc 136: 51-65
27. Torrång A (1987) Law of the iterated logarithm - cluster points of deterministic and random subsequences. Prob Math Stat 8: 133-141
28. Vasudeva R, Divanji G (1991) Law of the iterated logarithm for random subsequences. Stat Probab Letters 12: 189-194
29. Weiner D (1985) A maximal law of the iterated logarithm for operator-normalized stochastically compact partial sums of i.i.d. random vectors. In: Beck A (ed) Probability in Banach spaces V. Lecture Notes in Math 1153: 426-439
30. Zhang Bo (1995) LIL and SLLN for random sums. J Math Sci 76: 2335-2338