On the Iterated Martingale Transforms
2000 年 6 巻 2 号 p. 123-127
詳細
2000 年 6 巻 2 号 p. 123-127
Let f = (fn ,Fn )
n≥0 be a martingale on some filtered
complete probability space (Ω,F,P ) with
the usual conditions. We define the iterated martingale
transforms I (m)(f ) =
(In(m), (Fn
)) (m ≥1) with respect to f, the
discrete analogues of the iterated stochastic integrals.
We obtain the Lp (1≤p)-estimates
of I (m)(f )
||I (m)*||p ≤ (4mp)m ||S m (f )||p
and we also characterize a continuous martingale by the limit of the iterated martingale transforms.
