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A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part I: Foundation of the Method and Empirical Evidence

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(1)A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part I: Foundation of the Method and Empirical Evidence Denis Talay, Olivier Vaillant. To cite this version: Denis Talay, Olivier Vaillant. A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part I: Foundation of the Method and Empirical Evidence. [Research Report] RR-4326, INRIA. 2001, pp.28. �inria-00072261�. HAL Id: inria-00072261 https://hal.inria.fr/inria-00072261 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Part I: Foundation of the method and empirical evidence. Denis Talay — Olivier Vaillant. N° 4326 Novembre 2001. ISSN 0249-6399. ISRN INRIA/RR--4326--FR+ENG. THÈME 4. apport de recherche.

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(227) GAHI JsKiO Q SC >% >w@X@sB. = ;\<:=>?A@&BCEDXF G HI JsKiO T = ;X> S ]O @{> {@9BCEDXF G HI J(K ‰ >] w@&B ^= O T = Q S C> A> w@X@ ‰ >] {@ > ^ fgpr~ˆxj5|?ˆxj„~j5{•w!u+wpry}{~ƒs}}j©~Šw!~.wg?j1®ayPtztry+¼<pz{n{ud™}j·inj5wg?y  y€® ~pzi$s?tru€wpry}{E }µ.y}{~p  j5ˆ : = ˆxj„u}tzp„a u€wpry}{~ B  :y=B y€® unˆxu}{  y}i,™+u}ˆpvu€š?trj ‡ ¼<p¹wxgtvu­¼ ‰µ o    ”[µ  yPˆj„uP !g1pz{?pzwpvu€tP|u€ˆ!u€ikj5wj5ˆ Á+ 5y}{~p  j5ˆ : r pYµ pdµ  µˆ!u€{  yPi ™+u€ˆxpvu€š?trj„~  # > @ Á­¼<p¹wxg& yPikinyP{ | tru­¼ Š  > @ >WE@\])W Áu€{  j¿{?j·wxg?j›|u€ˆwpv trj›~ƒ‚[~ƒwj„i% Œ dee ]  #0$ & G > \@ O o  -&  G =   #%$ & G > \@{B  - $ & G > \@ x ]^? : t r G  7  : B f n o   t  #%$ & G >   @{B - $ & G >   @x ]  # B Äd”+l•Æ r eg o -&  = : r @>  #%$ & G >   @ O  # > T | | fg?j5{Á G Q S C>  > @X=@ < : o , &  = C t  #%$ & G > @ x > Äd”)}c Æ r# fg?pv~&tvu+wwj5ˆnu€|?|ˆy­†[priku€wpry}{6pv~

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