Stochastic integration in UMD Banach spaces
van Neerven, J. M. A. M. ; Veraar, M. C. ; Weis, L.
Ann. Probab., Tome 35 (2007) no. 1, p. 1438-1478 / Harvested from Project Euclid
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In this paper we construct a theory of stochastic integration of processes with values in ℒ(H, E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an H-cylindrical Brownian motion. Our approach is based on a two-sided Lp-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of ℒ(H, E)-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the Itô isometry, the Burkholder–Davis–Gundy inequalities, and the representation theorem for Brownian martingales.
Publié le : 2007-07-14
Classification:  Stochastic integration in Banach spaces,  UMD Banach spaces,  cylindrical Brownian motion,  γ-radonifying operators,  decoupling inequalities,  Burkholder–Davis–Gundy inequalities,  martingale representation theorem,  60H05,  28C20,  60B11 
@article{1181334250,
     author = {van Neerven, J. M. A. M. and Veraar, M. C. and Weis, L.},
     title = {Stochastic integration in UMD Banach spaces},
     journal = {Ann. Probab.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 1438-1478},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1181334250}
}

van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L. Stochastic integration in UMD Banach spaces. Ann. Probab., Tome 35 (2007) no. 1, pp.  1438-1478. http://gdmltest.u-ga.fr/item/1181334250/