Stochastic calculus for Brownian motion on a Brownian fracture

Authors
Khoshnevisan, D Lewis, TM
Citation
D. Khoshnevisan et Tm. Lewis, Stochastic calculus for Brownian motion on a Brownian fracture, ANN APPL PR, 9(3), 1999, pp. 629-667
Citations number
40
Categorie Soggetti
Mathematics
Journal title
ANNALS OF APPLIED PROBABILITY
ISSN journal
10505164 → ACNP
Volume
9
Issue
3
Year of publication
1999
Pages
629 - 667
Database
ISI
SICI code
1050-5164(199908)9:3<629:SCFBMO>2.0.ZU;2-O
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.