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dc.contributor.authorUmarov, Sabiren_US
dc.contributor.authorDaum, Fredericken_US
dc.contributor.authorNelson, Kenricen_US
dc.date.accessioned2018-05-10T17:14:54Z
dc.date.available2018-05-10T17:14:54Z
dc.date.issued2014-01-01
dc.identifier.citationSabir 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.
dc.identifier.issn1314-2224
dc.identifier.urihttps://hdl.handle.net/2144/28867
dc.description.abstractIn 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.en_US
dc.relation.ispartofFractional Calculus and Applied Analysis
dc.rightsPublished version: © 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subjectStochastic differential equationen_US
dc.subjectTime-changeen_US
dc.subjectApplied mathematicsen_US
dc.subjectFiltering problemen_US
dc.subjectZakai equationen_US
dc.subjectFractional order differential equationen_US
dc.subjectPseudo-differential operatoren_US
dc.subjectLévy processen_US
dc.subjectStable subordinatoren_US
dc.subjectStochastic calculusen_US
dc.titleFractional generalizations of filtering problems and their associated fractional Zakai equationsen_US
dc.typeArticleen_US
dc.identifier.doi10.2478/s13540-014-0197-x
pubs.elements-sourcecrossrefen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Engineeringen_US
pubs.organisational-groupBoston University, College of Engineering, Department of Electrical & Computer Engineeringen_US
pubs.publication-statusPublisheden_US


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Published version: © 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
Except where otherwise noted, this item's license is described as Published version: © 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.