Abstract
In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering problem emerges as the Riemann-Liouville or Caputo-Djrbashian fractional derivative in the associated Zakai equation. We discuss fractional generalizations of the nonlinear filtering problem whose state and observation processes are driven by time-changed Brownian motion or/and Lévy process.
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Umarov, S., Daum, F. & Nelson, K. Fractional generalizations of filtering problems and their associated fractional Zakai equations. Fract Calc Appl Anal 17, 745–764 (2014). https://doi.org/10.2478/s13540-014-0197-x
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DOI: https://doi.org/10.2478/s13540-014-0197-x