Abstract
We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise with Gauss measure rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the ‘order-disorder’ problem of Shiryayev.
Keywords
- Stochastic Differential Equation
- Cauchy Sequence
- Gauss Measure
- Additive Probability Measure
- Weak Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. N. SHIRYAYEV: Statistical Sequential Analysis, A.M.S. Translations of Mathematical Monography, Vol. 38, Providence, 1973.
M. L. DASHEVSKII and R. SH. LIPSTER: Simulation of Stochastic Differential Equations Connected with the "Disorder" problem by Means of Analogue Computers. Autmatikia i Telemekhanika Vol. 27, No. 4, 1966.
A. V. BALAKRISHNAN: A White Noise Version of the Girsanov Formula: Proceedings of the Symposium on Stochastic Differential Equations, Kyoto 1976, edited by K. Ito.
A. V. SKOROKHOD: Integration in Hilbert Space, Springer-Verlag, Berlin, Heidelberg, New York, 1974.
A. V. BALAKRISHNAN: Radon Nikodym Derivatives of a Class of Weak Distributions on Hilbert Spaces: Appl. Math Opt. 3 (1977) 209–225.
W. M. WONHAM: Some Applications of Stochastic Differential Equations to Optimal Non-linear Filtering, J. SIAM on Control, Ser. A, Vol. 2, No. 3, 1965.
R. S. LIPSTER and A. N. SHIRYAYEV: Statistics of Random Processes, Nauka 1975 (Russian).
E. WONG and M. ZAKZI: On the Relation Between Ordinary Integrals and Stochastic Integrals, Intern. J. of Engrg. Science, 3 (1965) p. 213–229.
R. L. STRATANOVICH: Conditioned Markov Processes and Their Application to Optimal Control, Elsevier, New York 1968.
K. ITO: Stochastic Differentials, Appl. Math. Opt. 1, (1976), 374–381.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Balakrishnan, A.V. (1978). Likelihood ratios with gauss measure noise models. In: Kallianpur, G., Kölzow, D. (eds) Measure Theory Applications to Stochastic Analysis. Lecture Notes in Mathematics, vol 695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062657
Download citation
DOI: https://doi.org/10.1007/BFb0062657
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09098-4
Online ISBN: 978-3-540-35556-4
eBook Packages: Springer Book Archive
