Stability of optimal filter higher-order derivatives

Vladislav Z.B. Tadić and Arnaud Doucet

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 4808-4858

Abstract: In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter first-order derivatives, the parameter can be estimated online. To analyze the asymptotic behavior of such methods, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. These properties are studied here. Under regularity conditions, we show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the same derivatives are geometrically ergodic.

Keywords: State-space models; Optimal filter; Optimal filter higher-order derivatives; Forgetting of initial conditions; Geometric ergodicity; Log-likelihood (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.02.001

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