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- W2059362614 abstract "Stroock and Yor have posed the following problem: let B be a Brownian motion and n∈N∗; which of the martingales Mn(t):=∫0tBsndBs are pure? In the case where n is odd, they have proved that Mn(.) is pure. Whether or not M2n is pure has remained an open question. We show that M2n is pure and consequently the filtration generated by a symmetric Bessel process of dimension between 1 and 2 is Brownian. Stroock et Yor ont posé le problème : soit B un mouvement brownien et n∈N∗ ; déterminer parmi les martingales Mn(t) :=∫0tBsndBs, celles qui sont pures. Dans le cas où n est impair, ils ont prouvé que Mn(.) est pure. La question pour M2n est restée ouverte. On montre que M2n est pure et par conséquent la filtration engendrée par un processus de Bessel symétrique de dimension comprise entre 1 et 2 est brownienne." @default.
- W2059362614 created "2016-06-24" @default.
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- W2059362614 date "2003-04-01" @default.
- W2059362614 modified "2023-09-25" @default.
- W2059362614 title "Some remarkable pure martingales" @default.
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- W2059362614 doi "https://doi.org/10.1016/s0246-0203(02)00018-3" @default.
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