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July, 2011 From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order
Francis HIRSCH, Bernard ROYNETTE, Marc YOR
J. Math. Soc. Japan 63(3): 887-917 (July, 2011). DOI: 10.2969/jmsj/06330887

Abstract

We present an Itô type formula for a Gaussian process, in which only the one-marginals of the Gaussian process are involved. Thus, this formula is well adapted to the study of processes increasing in the convex order, in a Gaussian framework. In particular, we give conditions ensuring that processes defined as integrals, with respect to one parameter, of exponentials of two-parameter Gaussian processes, are increasing in the convex order with respect to the other parameter. Finally, we construct Gaussian sheets allowing to exhibit martingales with the same one-marginals as the previously defined processes.

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Francis HIRSCH. Bernard ROYNETTE. Marc YOR. "From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order." J. Math. Soc. Japan 63 (3) 887 - 917, July, 2011. https://doi.org/10.2969/jmsj/06330887

Information

Published: July, 2011
First available in Project Euclid: 1 August 2011

zbMATH: 1233.60008
MathSciNet: MR2836749
Digital Object Identifier: 10.2969/jmsj/06330887

Subjects:
Primary: 60E15, 60G15
Secondary: 60G44, 60G48, 60G60

Rights: Copyright © 2011 Mathematical Society of Japan

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Vol.63 • No. 3 • July, 2011
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