The law of the iterated logarithm for extreme value of random elements in Banach lattices. (English. Ukrainian original) Zbl 0960.60009

Matsak, I. K.

Theory Probab. Math. Stat. 59, 129-138 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 125-134 (1998).

The author introduces the notions \(\lim\sup\{\cdot\}\) and \(\lim\inf\{\cdot\}\) in some infinite-dimensional spaces, namely, in separable Banach lattices. Using these notions the law of the iterated logarithm is generalized for these spaces. The law of the iterated logarithm for extremes of a sequence of normed random elements in a separable Banach lattice is proved. Similar problems were investigated by the author [Ukr. Math. J. 50, No. 9, 1405-1415 (1998); translation from Ukr. Mat. Zh. 50, No. 9, 1227-1235 (1998; Zbl 0941.60014)].

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
60F15	Strong limit theorems
60G10	Stationary stochastic processes

Keywords:

extreme elements in Banach grids; law of the iterated logarithm

Citations:

Zbl 0941.60014