Author URLs
Document Type
Article
Publication Date
2014
Subject: LCSH
Stochastic differential equations, Fractional calculus
Disciplines
Mathematics
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.
DOI
10.2478/s13540-014-0197-x
Repository Citation
Umarov, Sabir; Daum, Fred; and Nelson, Kenric, "Fractional Generalizations of Filtering Problems and Their Associated Fractional Zakai Equation" (2014). Mathematics Faculty Publications. 18.
https://digitalcommons.newhaven.edu/mathematics-facpubs/18
Publisher Citation
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.
Comments
MSC 2010 : Primary 60H10; Secondary 35S10, 60G51, 60H05
This is the final version of the article published in
Fract. Calc. Appl. Anal., 17
(3), pp. 745-764, watermarked for non-commercial sharing by the author. The original publication is located at http://dx.doi.org/10.2478/s13540-014-0197-x