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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
48 Modeling and In verse Problems in the Presence of Uncertainty
There are another two alternative and equivalent ways to define convergenc e
almost surely; that is, condition (2.117) can be r eplaced by either
lim
m→∞
Prob
\
jm
(|X
j
X| < ǫ)
= 1, for any positive number ǫ,
or
lim
m→∞
Prob
[
jm
(|X
j
X| ǫ)
= 0, for any positive number ǫ.
By the above equation, we easily see that convergence a.s. implies convergence
in probability, and thus implies convergence in distribution. In gener al, the
conve rse is not true; that is, convergence in probability does not imply conver-
gence almost surely. However, convergence in probability implies c onverg
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Publisher Resources

ISBN: 9781482206432