On the Martingale Representation with Respect to the super-Brownian Filtration
Christian Mandler, Ludger Overbeck
TL;DR
This paper derives an explicit martingale representation for square-integrable processes within the super-Brownian motion framework, utilizing a generalized Dupire derivative for superprocess functionals.
Contribution
It introduces a novel explicit form of the martingale representation for super-Brownian motion using an extended Dupire derivative.
Findings
Explicit martingale representation derived
Extension of Dupire derivative to superprocesses
Framework applicable to square-integrable superprocess martingales
Abstract
We derive the explicit form of the martingale representation for square-integrable processes that are martingales with respect to the natural filtration of the super-Brownian motion. This is done by using a weak extension of the Dupire derivative for functionals of superprocesses.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Probability and Risk Models