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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
224 Modeling and Inverse Problems in the Presence of Uncertainty
It can be shown that the Wiener process is a Gaussian process with mean
and covariance functions respectively given by (e.g., see [7 2, Theorem 3.2])
E(W (t)) = 0, C ov{W (t), W (s)} = min{t, s}. (7 .25)
This implies that for any fixed t, W (t) is Gaussian distributed with zero mean
and variance given by t; tha t is, W (t) N(0, t). By Theorem 7.1.1 and (7.25)
we know that a Wiener process is also m.s. continuous.
The sample path of the Wiener process has a number of interesting prop-
erties. For example, the sa mple path of a Wiener process is nowhere differ-
entiable (with probability ...
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Publisher Resources

ISBN: 9781482206432