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.

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

DOI

10.2478/s13540-014-0197-x

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.

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