Abstract: | Let (ξ
k
,F
k
) be a martingale difference sequence. The paper concerns the tail behavior of the quadratic formS
n
= ∑
k=1
n
∑
j=1
k−1
β
n
k−j
χ
k
χ
j
, where β
n
asn→∞. The main conclusions aboutP}n
−1
S
n
>x
n
}, wherex
n
→∞, asn→∞, are obtained using the tail behavior of a martingale with values in a certain Hilbert space.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 37, No. 4, pp. 532–549, October–December, 1997. |