Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 63, Number 3 (2011), 887-917.
From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order
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.
J. Math. Soc. Japan, Volume 63, Number 3 (2011), 887-917.
First available in Project Euclid: 1 August 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15: Inequalities; stochastic orderings 60G15: Gaussian processes
Secondary: 60G44: Martingales with continuous parameter 60G48: Generalizations of martingales 60G60: Random fields
HIRSCH, Francis; ROYNETTE, Bernard; YOR, Marc. From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order. J. Math. Soc. Japan 63 (2011), no. 3, 887--917. doi:10.2969/jmsj/06330887. https://projecteuclid.org/euclid.jmsj/1312203805