A Hilbertian approach for fluctuations on the McKean-Vlasov model

Begoña Fernandez and Sylvie Méléard

Stochastic Processes and their Applications, 1997, vol. 71, issue 1, 33-53

Abstract: We consider the sequence of fluctuation processes associated with the empirical measures of the interacting particle system approximating the d-dimensional McKean-Vlasov equation and prove that they are tight as continuous processes with values in a precise weighted Sobolev space. More precisely, we prove that these fluctuations belong uniformly (with respect to the size of the system and to time) to W-(1+D), 2D0 and converge in C([0, T], W-(2+2D), D0) to a Ornstein-Uhlenbeck process obtained as the solution of a Langevin equation in W-(4+2D), D0, where D is equal to 1 + [d/2]. It appears in the proofs that the spaces W-(1 --> D), 2D0 and W-(2-2D), D0 are minimal Sobolev spaces in which to immerse the fluctuations, which was our aim following a physical point of view.

Keywords: Convergence; of; fluctuations; McKean-Vlasov; equation; Weighted; Sobolev; spaces (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00067-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:71:y:1997:i:1:p:33-53

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().