Journal of Mathematics of Kyoto University

A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet

Francis Hirsch and Marc Yor

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Abstract

We give some adequate extension, in the framework of a general Lévy process, of our previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The Lévy process framework allows us to streamline our previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. We give some illustrations of our construction when the Lévy process is either a Gamma process, or a Poisson process. We also work in the fractional Brownian and stable frameworks.

Article information

Source
J. Math. Kyoto Univ., Volume 49, Number 4 (2009), 785-815.

Dates
First available in Project Euclid: 11 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1265899483

Digital Object Identifier
doi:10.1215/kjm/1265899483

Mathematical Reviews number (MathSciNet)
MR2591117

Zentralblatt MATH identifier
1191.60040

Subjects
Primary: 60Gxx: Stochastic processes 60Hxx: Stochastic analysis [See also 58J65]

Citation

Hirsch, Francis; Yor, Marc. A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet. J. Math. Kyoto Univ. 49 (2009), no. 4, 785--815. doi:10.1215/kjm/1265899483. https://projecteuclid.org/euclid.kjm/1265899483


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