ALMOST SURE LIMIT POINTS FOR DELAYED RANDOM SUMS
Keywords:Law of iterated logarithm, Delayed sums, Delayed random sums, Asymmetric stable law, Almost sure limit points
Let be a sequence of i.i.d. positive asymmetric stable random variables with a common distribution function F with index ,. The present work intends to obtain almost sure limit points for a sequence of properly normalized delayed random sums.
Chover, J. (1966). A law of iterated logarithm for stable summands, Proc. Amer. Math.
GootyDivanji (2004). Law of iterated logarithm for subsequences of partial sums which
are in the domain of partial attraction of semi stable law, Probability and Mathematical
Statistics, Vol.24, Fasc. 2,41, 433-442.
GootyDivanji and K.N.Raviprakash (2016).A log log law for delayed random sums, preprint.
Heyde, C.C. (1967). On large deviation problems for sums of random variables which are
not attracted to the normal law, Ann. Math. Statist. 38(5):1575-1578.
Lai, T.L. (1973). Limit theorems for delayed sums. Ann.Probab.2,432-440.
Nielsen, O.B. (1961). On the rate of growth of the partial maxima of a sequence of
independent identically distributed random variables, Math.Scand 9:383-394.
Spitzer, F (1964). Principles of random walk, Van Nostrand: Princeton, New Jercey.
Vasudeva, R and Divanji, G (1991). Law of iterated logarithm for random subsequences,
Statistics and Probability letters 12:189-194.
Vasudeva, R and Divanji, G (1993). The law of the iterated logarithm for delayed sums
under a nonidentically distributed setup, Theory Probab. Appl., 37(3), 497-506.
How to Cite
Copyright (c) 2021 International Education and Research Journal (IERJ)
This work is licensed under a Creative Commons Attribution 4.0 International License.