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Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time Read chapter Read first chapter

2019 | OriginalPaper | Chapter

9. Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models

Author : Albert N. Shiryaev

Published in: Stochastic Disorder Problems

Publisher: Springer International Publishing

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Abstract

1. Suppose that we observe the stochastic process \(X=(X_t)_{t \geqslant 0}\),
$$\displaystyle X_t=\theta \mu t+B_t, \quad X_0=0, $$
on the filtered probability space https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-01526-8_9/369561_1_En_9_IEq2_HTML.gif , where \(B=(B_t)_{t \geqslant 0}\) is the standard Brownian motion (as a martingale with respect to the filtration flow \((\mathcal {F}_t)_{t \geqslant 0}\), EB t = 0 and \(\mathrm {E} B_t^2=t\)).

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previous chapter Disorder on Filtered Probability Spaces
next chapter Some Applications to Financial Mathematics
Footnotes
1
Alternative terminology: “distinguishing between two hypotheses”.
 
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Metadata
Title
Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models
Author
Albert N. Shiryaev
Copyright Year
2019
Book
Stochastic Disorder Problems

Print ISBN: 978-3-030-01525-1

Electronic ISBN: 978-3-030-01526-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-01526-8_9