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Advances in Pure and Applied Mathematics

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1869-6090
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Martingale characterizations of increment processes in a commutative hypergroup

Herbert Heyer
  • Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany. E-mail:
  • Other articles by this author:
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/ Gyula Pap
  • Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary. E-mail:
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Published Online: 2010-03-18 | DOI: https://doi.org/10.1515/apam.2010.008

Abstract

Martingale characterizations and the related martingale problem are studied for increments processes with values in a commutative hypergroup. For the proofs Fourier theory is applied for the convolution hemigroups associated with the increment processes.

Keywords.: Commutative hypergroups; increment processes; martingale characterizations; Fourier transform; convolution hemigroups; hemigroups and processes of finite variation; Gaussian and diffusion hemigroups and processes; Sturm–Liouville hypergroups; Bessel–Kingman hypergroups

About the article

Received: 2008-07-12

Revised: 2008-12-07

Published Online: 2010-03-18

Published in Print: 2010-03-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2010.008.

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