A complete characterization of local martingales which are functions of Brownian motion and its maximum

Obloj, Jan

Obloj, Jan

Bernoulli, Tome 12 (2006) no. 2, p. 955-969 / Harvested from Project Euclid

Résumé

We prove the max-martingale conjecture of Obłój and Yor. We show that for a continuous local martingale [math] and a function [math] , [math] is a local martingale if and only if there exists a locally integrable function [math] such that [math] . This readily implies, via Lévy's equivalence theorem, an analogous result with the maximum process replaced by the local time at [math] .

Publié le : 2006-12-14
Classification: Azéma-Yor martingales, continuous martingales, maximum process, max-martingales, Motoo's theorem

@article{1165269146,
     author = {Obloj, Jan},
     title = {A complete characterization of local martingales which are functions of Brownian motion and its maximum},
     journal = {Bernoulli},
     volume = {12},
     number = {2},
     year = {2006},
     pages = { 955-969},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1165269146}
}

Obloj, Jan. A complete characterization of local martingales which are functions of Brownian motion and its maximum. Bernoulli, Tome 12 (2006) no. 2, pp.  955-969. http://gdmltest.u-ga.fr/item/1165269146/