Fractional generalizations of filtering problems and their associated fractional Zakai equations
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Citation (published version)Sabir Umarov, Frederick Daum, Kenric Nelson. 2014. "Fractional generalizations of filtering problems and their associated fractional Zakai equations." Fractional Calculus and Applied Analysis, Volume 17, Issue 3, Pages 745–764. DOI: https://doi.org/10.2478/s13540-014-0197-x.
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.
RightsPublished version: © 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.