A weak law for normed weighted sums of random elements in rademacher type p banach spaces
For weighted sums Σ j = 1 n a j V j of independent random elements { V n , n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form ( Σ j = 1 na jV j − v n) b n → p 0 is established, where { v n , n ≥ 1} and b n → ∞ are suitable sequences...
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Published in | Journal of multivariate analysis Vol. 37; no. 2; pp. 259 - 268 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
San Diego, CA
Elsevier Inc
01.05.1991
Elsevier |
Series | Journal of Multivariate Analysis |
Subjects | |
Online Access | Get full text |
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Summary: | For weighted sums Σ
j = 1
n
a
j
V
j
of independent random elements {
V
n
,
n ≥ 1} in real separable, Rademacher type
p (1 ≤
p ≤ 2) Banach spaces, a general weak law of large numbers of the form
(
Σ
j = 1
na
jV
j − v
n)
b
n
→
p 0
is established, where {
v
n
,
n ≥ 1} and
b
n
→ ∞ are suitable sequences. It is assumed that {
V
n
,
n ≥ 1} is stochastically dominated by a random element
V, and the hypotheses involve both the behavior of the tail of the distribution of |
V| and the growth behaviors of the constants {
a
n
,
n ≥ 1} and {
b
n
,
n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {
V
n
,
n >- 1}. |
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ISSN: | 0047-259X 1095-7243 |
DOI: | 10.1016/0047-259X(91)90083-E |