[Flows of kernels and coalescing flows]
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.
Accepted:
Published online:
Yves Le Jan 1; Olivier Raimond 1
@article{CRMATH_2003__336_2_181_0, author = {Yves Le Jan and Olivier Raimond}, title = {Flots de noyaux et flots coalescents}, journal = {Comptes Rendus. Math\'ematique}, pages = {181--184}, publisher = {Elsevier}, volume = {336}, number = {2}, year = {2003}, doi = {10.1016/S1631-073X(03)00004-9}, language = {fr}, }
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/
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