The Law of the Iterated Logarithm for $B$-Valued Random Variables with Multidimensional Indices

Li, Deli; Wu, Zhi‐Quan

doi:10.1214/aop/1176991425

Cited by 14 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note in this connection the work of Smythe (1973Smythe ( , 1974, Gut (1978Gut ( , 1980, and Lagodowski and Rychlik (1985) on the laws of large numbers, and the papers of Wichura (1973), Li and Wu (1989), Adler (1992), and Li et al (1992) on the law of iterated logarithm for certain partial sums of the independent random variables indexed on K r , the set of all r-dimensional vectors with positive integers as entries. During roughly the same period, building on earlier work of Gnedenko (1943) and Barndorff-Nielsen (1963), a number of authors have studied the stability properties of sample maxima, and other large order statistics, of a sequence of independent identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 95%

Stability of Maxima of Random Variables with Multidimensional Indices

Tomkins

2004

Extremes

View full text Add to dashboard Cite

The paper discusses the stability of suitably-defined maxima of a set of i.i.d. random variables with multidimensional indices. It is shown that theorems of Gnedenko (1943) and Tomkins (1986) concerning relative stability and complete relative stability of maxima remain valid in the new setting. Moreover, a criterion for almost sure relative stability for maxima with multidimensional indices is presented, extending a result of Barndorff-Nielsen (1963).

show abstract