Continuous local martingales and stochastic integration in UMD Banach spaces

Continuous local martingales and stochastic integration in UMD Banach spaces

Veraar, M.C.

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics

2007-12-01

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We give several characterizations of integrability and prove a version of the Itô isometry, the Burkholder-Davis-Gundy inequality, the Itô formula and the martingale representation theorem.

stochastic integration in Banach spaces
continuous local martingales
UMD Banach spaces
random time change
y-radonifying operators
Burkholder-Davis-Gundy
inequalities
Itô formula
martingale representation theorem

http://resolver.tudelft.nl/uuid:c95d590d-ad43-41d5-92d1-2b15d9941ca6

Taylor and Francis, http://www.tandf.co.uk/journals

1744-2508

Stochastics, 79 (2007), no.6, p. 601-618

Institutional Repository

journal article

(c) 2007 Taylor and Francis