Periodica Mathematica Hungarica
Volume/Issue:
Volume 61: Issue 1-2
Applying Itô’s motto: “Look at the infinite dimensional picture” by constructing sheets to obtain processes increasing in the convex order
Authors:
Francis Hirsch Laboratoire d’Analyse et Probabilités, Université d’Évry Val d’Essonne, Boulevard F. Mitterrand, F-91025 Évry Cedex, France

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Bernard Roynette Institut Elie Cartan, Université Henri Poincaré, B.P. 239, F-54506 Vandœuvre-lès-Nancy Cedex, France

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Marc Yor Institut Universitaire de France, Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 Place Jussieu — Case 188, F-75252 Paris Cedex 05, France

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Pages:
195–211
Online Publication Date:
01 Oct 2010
Publication Date:
01 Sep 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10998-010-3195-8
Keywords:
60E15; 60G44; 60G48; 60G60; 60G15; 60G51; convex order; 1-martingale; PCOC; Lévy sheet; Sato sheet; Gaussian sheet
Restricted access

Abstract  

Strongly inspired by the result due to Carr-Ewald-Xiao that the arithmetic average of geometric Brownian motion is an increasing process in the convex order, we extend this result to integrals of Lévy processes and Gaussian processes. Our method consists in finding an appropriate sheet associated to the original Lévy or Gaussian process, from which the one-dimensional marginals of the integrals will appear to be those of a martingale, thus proving the increase in the convex order property.

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Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1971
Volumes
per Year		 2
Issues
per Year		 4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address		 H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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