An extension of the Lévy characterization to fractional Brownian motion
Mishura, Yuliya ; Valkeila, Esko
Ann. Probab., Tome 39 (2011) no. 1, p. 439-470 / Harvested from Project Euclid
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Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Ω, F, P). The classical characterization due to P. Lévy says that X is a Brownian motion if and only if X and Xt2 − t, t ≥ 0, are martingales with respect to the intrinsic filtration FX. We extend this result to fractional Brownian motion.
Publié le : 2011-03-15
Classification:  Fractional Brownian motion,  Lévy theorem,  60G15,  60E05,  60H99 
@article{1298669170,
     author = {Mishura, Yuliya and Valkeila, Esko},
     title = {An extension of the L\'evy characterization to fractional Brownian motion},
     journal = {Ann. Probab.},
     volume = {39},
     number = {1},
     year = {2011},
     pages = { 439-470},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1298669170}
}

Mishura, Yuliya; Valkeila, Esko. An extension of the Lévy characterization to fractional Brownian motion. Ann. Probab., Tome 39 (2011) no. 1, pp.  439-470. http://gdmltest.u-ga.fr/item/1298669170/