Abstract
Suppose that the nonlinear filtering equations are solved using an incorrect initial condition. It is known that the relative entropy of the actual conditional distribution with respect to this incorrectly initialized filter is a positive supermartingale. In this paper, we study the filtering of diffusion signals. Using the Kushner-Stratonovich equations, we decompose the relative entropy supermartingale into decreasing and local martingale terms, and we derive an entropy bound on information and error measures of the difference between conditional distribution and incorrectly initialized filter.
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Ocone, D. (1999). Entropy Inequalities and Entropy Dynamics in Nonlinear Filtering of Diffusion Processes. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_28
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_28
Publisher Name: Birkhäuser, Boston, MA
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