Stochastic calculus for Brownian motion on a Brownian fracture

Authors
Khoshnevisan, Davar M. Lewis, Thomas
Citation
Khoshnevisan, Davar et M. Lewis, Thomas, Stochastic calculus for Brownian motion on a Brownian fracture, Annals of applied probability , 9(3), 1999, pp. 629-667
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
9
Issue
3
Year of publication
1999
Pages
629 - 667
Database
ACNP
SICI code
Abstract
In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.