Comptes Rendus
Probabilités
Flots de noyaux et flots coalescents
[Flows of kernels and coalescing flows]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 181-184.

We present a part of the results of Le Jan and Raimond (math.PR/9909147). We show that starting with a compatible family of Feller semigroups, one can construct a stochastic flow of kernels. Under an additional hypotheses (on the 2-points motion), we show that it is possible to associate to a flow of kernels a coalescing flow such that the flow of kernels can be obtained by filtering the coalescing flow with respect to a sub-noise of an extension of the noise generated by the coalescing flow.

Nous présentons une partie des résultats de Le Jan et Raimond (math.PR/0203221). Nous montrons comment à partir d'une famille compatible de semigroupes felleriens, on peut construire un flot stochastique de noyaux. Sous une hypothèse supplémentaire (sur le mouvement de deux points), nous montrons qu'à un flot de noyaux, il est possible d'associer un flot coalescent tel que le flot de noyaux puisse être construit en filtrant ce flot coalescent par un sous-bruit d'une extension du bruit engendré par le flot coalescent.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00004-9

Yves Le Jan 1; Olivier Raimond 1

1 Université Paris Sud, mathématiques, bât 425, 91405 Orsay, France
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Yves Le Jan; Olivier Raimond. Flots de noyaux et flots coalescents. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 181-184. doi : 10.1016/S1631-073X(03)00004-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00004-9/

[1] R. Arratia, Brownian motion on the line, Ph.D. Thesis, University of Wisconsin, Madison, 1979

[2] Y. Le Jan, O. Raimond, Integration of Brownian vector fields, to appear in Ann. Probab. or | arXiv

[3] Y. Le Jan; O. Raimond Une classification des flots solutions d'une EDS, C. R. Acad. Sci. Paris Sér. I, Volume 336 (2003)

[4] J.G. Propp; D.B. Wilson Exact sampling with coupled Markov chains and applications to statistical mechanics, in: Proceedings of the Seventh International Conference on Random Structures and Algorithms, Atlanta, GA, 1995, Random Structures Algorithms, Volume 9 (1996) no. 1–2, pp. 223-252

[5] B. Tsirelson, Unitary Brownian motions are linearizable, 1998, . Also MSRI Preprint No. 1998-027 | arXiv

[6] S. Watanabe The stochastic flow and the noise associated to Tanaka's stochastic differential equation, Ukraı̈n. Mat. Zh., Volume 52 (2000) no. 9, pp. 1176-1193 English translation: Ukrainian Math. J. 52 (9) (2001) 1346–1365

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