Skip to Main Content
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
234 Modeling and Inverse Problems in the Presence of Uncertainty
The above theorem implies that if a sa mple-continuous martingale has finite
variatio n, then it must be a constant. It is worth no ting that there exist some
martingales with finite variation. But by Theorem 7.1.10, we k now that such
martingales must be sample discontinuous . An example of such martingales
is {X(t) λt : t 0}, where {X(t) : t 0} is a Poisson process with rate λ.
7.1.6.1 Examples of Sample-Continuous Martingales
Let F
t
be the σ-algebra generated by {W (s) : 0 s t}. Then by the
definition of the Wiener process, it can be shown that the Wiener process is
a martingale with r espe ct to {F
t
}. Specifically, by Jensen’s inequality (2 .67)
and W (t) N(0, t) we find that ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Nonlinear Inverse Problems in Imaging

Nonlinear Inverse Problems in Imaging

Jin Keun Seo, Eung Je Woo
Multimodal Scene Understanding

Multimodal Scene Understanding

Michael Ying Yang, Bodo Rosenhahn, Vittorio Murino

Publisher Resources

ISBN: 9781482206432