Stochastic diﬀerential equations, Fractional calculus
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.
Umarov, Sabir; Daum, Fred; and Nelson, Kenric, "Fractional Generalizations of Filtering Problems and Their Associated Fractional Zakai Equation" (2014). Mathematics Faculty Publications. 18.
Umarov, S., Daum, F. & Nelson, K. (2014). Fractional generalizations of filtering problems and their associated fractional Zakai equations. Frac. Calc. and Appl. Anal., 17(3): 745–764.