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Let {Xn; n ≥ 1} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides con- ditions under which the series ∑i≤n Xi converges almost surely and the tail series {Tn = ∑i≫n Xi; n ≥ 1} satisfies supk≥n ∥Tk∥= OP (bn) and supk≥n ∥Tk∥ / Bn P→ 0 for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].
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참고문헌 (12)
참고문헌 신청
A. Rosalsky / 1997 / On the rate of convergence of series of Banach space valued random elements / Nonlinear Anal 30 (7) : 4237 ~ 4248
A. Rosalsky / 1998 / On convergence of series of random variables with applications to martingale convergence and to convergence of series with orthogonal summands / Stoch. A
A. Rosalsky / 2001 / On convergence of series of random elements via maxi-mal moment relations with applications to martingale convergence and to convergence of series with p
A. Rosalsky / 2003 / On convergence of series of random elements via maxi-mal moment relations with applications to martingale convergence and to convergence of series with
E. Nam / 1996 / On the rate of convergence of series of random variables / Theory Probab. Math. Statist 52 : 129 ~ 140
A. Rosalsky / 1998 / On convergence of series of random variables with applications to martingale convergence and to convergence of series with orthogonal summands / Stoch. A
A. Rosalsky / 2001 / On convergence of series of random elements via maxi-mal moment relations with applications to martingale convergence and to convergence of series with p
A. Rosalsky / 2003 / On convergence of series of random elements via maxi-mal moment relations with applications to martingale convergence and to convergence of series with
E. Nam / 1996 / On the rate of convergence of series of random variables / Theory Probab. Math. Statist 52 : 129 ~ 140
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