Lévy area of Wiener processes in Banach spaces
Ledoux, M. ; Lyons, T. ; Qian, Z.
Ann. Probab., Tome 30 (2002) no. 1, p. 546-578 / Harvested from Project Euclid
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The goal of this paper is to construct canonical Lévy area processes for Banach space valued Brownian motions via dyadic approximations. The significance of the existence of canonical Lévy area processes is that a (stochastic) integration theory can be established for such Brownian motions (in Banach spaces). Existence of flows for stochastic differential equations with infinite dimensional noise then follows via the results of Lyons and Lyons and Qian. This investigation involves a careful analysis on the choice of tensor norms, motivated by the applications to infinite dimensional stochastic differential equations.
Publié le : 2002-04-14
Classification:  Brownian motion,  differential equation,  Gaussian comparison theorem,  Gaussian measure,  rough path,  60H10,  60H15,  60J60,  60G15 
@article{1023481002,
     author = {Ledoux, M. and Lyons, T. and Qian, Z.},
     title = {L\'evy area of Wiener processes in Banach spaces},
     journal = {Ann. Probab.},
     volume = {30},
     number = {1},
     year = {2002},
     pages = { 546-578},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1023481002}
}

Ledoux, M.; Lyons, T.; Qian, Z. Lévy area of Wiener processes in Banach spaces. Ann. Probab., Tome 30 (2002) no. 1, pp.  546-578. http://gdmltest.u-ga.fr/item/1023481002/