Abstract
This paper is concerned with information structure of the observation with additive non-Gaussian noise under the assumption that the noise belongs to a class of continuous martingales. It is known that such an observation is decomposed into a process with additive Gaussian noise and the quadratic covariation process of the additive noise. It is also known that the innovations process is decomposed into a standard Brownian motion process and the quadratic covariation process. In this paper, a number of sufficient conditions are obtained for the observation to have the information structure such that the information in the quadratic covariation process is not contained in the additive Gaussian part of the observation and/or the Brownian motion part of the innovation process.
Keywords
- Innovation Process
- Additive Noise
- Innovation Problem
- Additive Gaussian Noise
- Complete Probability Space
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References
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© 1990 Springer-Verlag
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Takeuchi, Y. (1990). On the decompositions of observations with non-Gaussian additive noise and their innovations processes. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120047
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DOI: https://doi.org/10.1007/BFb0120047
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