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Stability of the Filter Equation for a Time-Dependent Signal on ℝd

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Abstract

Stability of the pathwise filter equation for a time-dependent signal process induced by a d-dimensional stochastic differential equation and a linear observation is studied, using a variational approach introduced in [16]. A lower bound for the rate of stability is identified in terms of the mass-gap of a parabolic ground state transform associated with the generator of the signal process and the square of the observation. The lower bound can be easily calculated a priori and provides hints on how precisely to measure the signal in order to reach a certain rate of stability. Ergodicity of the signal process is not needed.

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  1. Fakultat fur Mathematik, Universitat Bielefeld, Postfach 100131, 33501 Bielefeld , Germany

    Wilhelm Stannat

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  1. Wilhelm Stannat
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Correspondence to Wilhelm Stannat.

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Stannat, W. Stability of the Filter Equation for a Time-Dependent Signal on ℝd. Appl Math Optim 52, 39–71 (2005). https://doi.org/10.1007/s00245-005-0820-7

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  • DOI: https://doi.org/10.1007/s00245-005-0820-7

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