Functional laws of the iterated logarithm for bivariate sums

Vasudeva, R. (1987) Functional laws of the iterated logarithm for bivariate sums. Sankhyā Ser. A, 49 (2). pp. 232-247.

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Abstract

"Let (Xn, n≥1) be a sequence of independent identically distributed random variables and let X+n=max(Xn,0), X−n=max(−Xn,0). Define Sn=∑nj=1Xj, S+n=∑nj=1X+j and S−n=∑nj=1X−j, n≥1. Assume that there exists a sequence (Bn) of positive constants such that the sequence {B−1nSn} converges weakly to a stable random variable with exponent α, 0<α<1. For any t∈[0,1] and n≥3, define ξn(t)={(B−1nS+[nt])1/loglogn,(B−1nS−[nt])1/loglogn}. In this paper the set of all almost sure limit functions of (ξn(⋅)) is obtained under the M1-topology. A similar functional law is obtained for the sequence of normalised partial sum processes of independent identically distributed random vectors of nonnegative independent components. Further, under certain conditions on X1, the set of all almost sure limit functions of the sequence {|B−1nS[nt]|1/loglogn, t∈[0,1]}, n≥3, is obtained.''

Item Type: Article
Subjects: Physical Sciences > Mathematics
Divisions: PG Campuses > Manasagangotri, Mysore > Mathematics
Depositing User: Kodandarama
Date Deposited: 21 May 2013 07:50
Last Modified: 21 May 2013 07:50
URI: http://eprints.uni-mysore.ac.in/id/eprint/9810

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