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Résumé On étudie les espaces mesurables G tels que le lemme de mesurabilité de Doob soit valable en toute généralité pour des fonctions à valeurs dans G.
In this paper, we find necessary and sufficient conditions for the finiteness of the integral functionals of the Bessel process: ∝ot f(Rs) ds, 0≤t<∞. They are in the form of a zero-one law and can be regarded as a counterpart of the They are in the form of a zero-one law and can be regarded as a counterpart of the Engelbert-Schmidt (1981) results, in the case of the Bessel process with...
Suppose that pathwise uniqueness holds for the SDE Xt=x0+3 £ot σ(Xs)dBs where |σ is bounded and bounded away from 0, and B is a Brownian motion on a filtered probability space, (Ω,F,Ft,P). We give conditions under which pathwise uniqueness continues to hold in the enlarged filtration (FtL), where L is the end of an (Ft)-optional set.
In this paper, we associate to a one-dimensional Brownian motion (Xt)t≥0, starting from 0, another Brownian motion: $$\tilde X_t = X_t - \int_0^t {\tfrac{1}{s}X_s ds (t \geqslant 0)} $$ . We remark that, for every t>0, σ( $$\tilde X_s $$ , s≤t) coïncides, up to negligible sets, with the σ-field generated by the Brownian bridge $$\left( {X_s - \frac{s}{t}X_t , s \leqslant t} \right)$$ . We study...
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