[A classification of the flows solution of a SDE]
Under general hypotheses, we show that the flows of kernels can be associated to a stochastic differential equation (SDE). We also show a classification theorem of the solutions of the SDE: they can be obtained through filtering the coalescing solution with respect to a sub-noise containing the white noise driving the SDE. The example of the isotropic flows is studied.
Sous des hypothèses assez générales, nous montrons que les flots de noyaux peuvent être associés à une équation différentielle stochastique (EDS). Nous montrons aussi un théorème de classification des solutions d'une EDS : elles peuvent être obtenues en filtrant la solution coalescente par un sous-bruit contenant le bruit blanc dirigeant l'EDS. L'exemple des flots isotropes est étudié.
Accepted:
Published online:
Yves Le Jan 1; Olivier Raimond 1
@article{CRMATH_2003__336_3_273_0,
author = {Yves Le Jan and Olivier Raimond},
title = {Une classification des flots solutions d'une {EDS}},
journal = {Comptes Rendus. Math\'ematique},
pages = {273--276},
publisher = {Elsevier},
volume = {336},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00005-0},
language = {fr},
}
Yves Le Jan; Olivier Raimond. Une classification des flots solutions d'une EDS. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 273-276. doi : 10.1016/S1631-073X(03)00005-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00005-0/
[1] Probability and Measure, Wiley Ser. Probab. Math. Statist., Wiley, New York, 1986
[2] Integration of Brownian vector fields, Ann. Probab., Volume 30 (2002) no. 2, pp. 826-873
[3] Y. Le Jan, O. Raimond, Flows, coalescence and noise, | arXiv
[4] Flots de noyaux et flots coalescents, C. R. Acad. Sci. Paris, Sér. I, Volume 336 (2003)
[5] B. Tsirelson, Unitary Brownian motions are linearizable, . Also MSRI Preprint No. 1998-027, 1998 | arXiv
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