Optimal speed of detection in generalized Wiener disorder problems
We define a general Wiener disorder problem in which a sudden change in a time profile of unknown size has to be detected in white noise of small intensity. Since both the time of the change and its size are unknown, this problem is considerably harder than standard Wiener disorder problems where the size of the change is assumed to be known a priori. We formulate the problem within the Bayesian framework of nonlinear filtering theory, and use Strassen's functional law of the iterated logarithm to bound stochastic measures which arise in the nonlinear filtering equations. This leads to explicit expressions for the detection delay in the optimal statistics for small noise intensities, and we indicate how these can be used to analyse the detection delays of recursive suboptimal detection algorithms for this problem.
Year of publication: |
2001
|
---|---|
Authors: | Vellekoop, M. H. ; Clark, J. M. C. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 95.2001, 1, p. 25-54
|
Publisher: |
Elsevier |
Keywords: | Wiener disorder problem Detection problems Nonlinear filtering Large deviations |
Saved in:
Saved in favorites
Similar items by person
-
Efficient Pricing of Derivatives on Assets with Discrete Dividends
Vellekoop, M. H., (2006)
-
Symmetries in jump-diffusion models with applications in option pricing and credit risk
Hoogland, J. K., (2003)
-
THE EARLY EXERCISE PREMIUM FOR THE AMERICAN PUT UNDER DISCRETE DIVIDENDS
Göttsche, O. E., (2011)
- More ...