메뉴 건너뛰기




Volumn 118, Issue 2, 2008, Pages 284-318

A wavelet particle approximation for McKean-Vlasov and 2D-Navier-Stokes statistical solutions

Author keywords

2D Navier Stokes equation; McKean Vlasov equation; Numerical discretization scheme of SDEs; Statistical solution; Stochastic particle approximation; Wavelet regression estimator

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; NAVIER STOKES EQUATIONS; PARAMETERIZATION; RANDOM PROCESSES; STATISTICAL METHODS; TURBULENCE;

EID: 37249018980     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2007.04.008     Document Type: Article
Times cited : (4)

References (25)
  • 2
    • 0000022835 scopus 로고
    • Invariant measures and evolution equations for Markov processes characterized via martingale problems
    • Bhatt A.G., and Karandikar R.L. Invariant measures and evolution equations for Markov processes characterized via martingale problems. Ann. Probab. 21 4 (1993) 2246-2268
    • (1993) Ann. Probab. , vol.21 , Issue.4 , pp. 2246-2268
    • Bhatt, A.G.1    Karandikar, R.L.2
  • 3
    • 0842277599 scopus 로고
    • Théorie de l'estimation fonctionnelle
    • Ecole Nationale de la Statistique et de l'Administration Economique et Centre d'Etudes des Programmes Economiques
    • Bosq D., and Lecoutre J.-P. Théorie de l'estimation fonctionnelle. Economica (1987) Ecole Nationale de la Statistique et de l'Administration Economique et Centre d'Etudes des Programmes Economiques
    • (1987) Economica
    • Bosq, D.1    Lecoutre, J.-P.2
  • 4
    • 37249016604 scopus 로고    scopus 로고
    • M. Bossy, Vitesse de convergence d'algorithmes particulaires stochastiques et application à l'équation de Burgers. Ph.D. Thesis, Aix-en-Provence 1, 1995
  • 5
    • 0031495979 scopus 로고    scopus 로고
    • Statistical solutions of the Navier-Stokes equations on the phase space of vorticity and the inviscid limit
    • Constantin P., and Wu J. Statistical solutions of the Navier-Stokes equations on the phase space of vorticity and the inviscid limit. J. Math. Phys. 38 6 (1997) 3031-3045
    • (1997) J. Math. Phys. , vol.38 , Issue.6 , pp. 3031-3045
    • Constantin, P.1    Wu, J.2
  • 8
    • 0001529786 scopus 로고
    • Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator
    • Dvoretsky A., Kiefer J., and Wolfowitz J. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Stat. 27 (1956) 642-669
    • (1956) Ann. Math. Stat. , vol.27 , pp. 642-669
    • Dvoretsky, A.1    Kiefer, J.2    Wolfowitz, J.3
  • 10
    • 0003352140 scopus 로고    scopus 로고
    • Diffusion processes associated with nonlinear evolution equations for signed initial measures
    • Jourdain B. Diffusion processes associated with nonlinear evolution equations for signed initial measures. Methodol. Comput. Appl. Probab. 2 1 (2000) 69-91
    • (2000) Methodol. Comput. Appl. Probab. , vol.2 , Issue.1 , pp. 69-91
    • Jourdain, B.1
  • 11
    • 33747349435 scopus 로고    scopus 로고
    • Regression in random design and warped wavelets
    • Kerkyacharian G., and Picard D. Regression in random design and warped wavelets. Bernoulli 10 6 (2004) 1053-1105
    • (2004) Bernoulli , vol.10 , Issue.6 , pp. 1053-1105
    • Kerkyacharian, G.1    Picard, D.2
  • 12
    • 0000254487 scopus 로고
    • Stochastic differential equations and stochastic flows of diffeomorphisms
    • Ecole d'Eté de probabilités de Saint-Flour XII, Springer
    • Kunita H. Stochastic differential equations and stochastic flows of diffeomorphisms. Ecole d'Eté de probabilités de Saint-Flour XII. Lectures Notes in Math. vol. 1097 (1982), Springer 143-303
    • (1982) Lectures Notes in Math. , vol.1097 , pp. 143-303
    • Kunita, H.1
  • 14
    • 0000852622 scopus 로고
    • Hydrodynamics in two dimensions and vortex theory
    • Marchioro C., and Pulvirenti M. Hydrodynamics in two dimensions and vortex theory. Comm. Math. Phys. 84 (1982) 483-503
    • (1982) Comm. Math. Phys. , vol.84 , pp. 483-503
    • Marchioro, C.1    Pulvirenti, M.2
  • 15
    • 0034310130 scopus 로고    scopus 로고
    • A trajectorial proof of the vortex method for the two-dimensional Navier-Stokes equation
    • Méléard S. A trajectorial proof of the vortex method for the two-dimensional Navier-Stokes equation. Ann. Appl. Probab. 10 4 (2000) 1197-1211
    • (2000) Ann. Appl. Probab. , vol.10 , Issue.4 , pp. 1197-1211
    • Méléard, S.1
  • 16
    • 37249000030 scopus 로고    scopus 로고
    • S. Méléard, Stochastic particle approximations for two-dimensional Navier-Stokes equations, Preprint Modal'X, II Workshop on Dynamics and Randomness, 12 2002
  • 17
    • 0003311631 scopus 로고    scopus 로고
    • Asymptotic behaviour of some interacting particle systems, McKean-Vlasov and Boltzmann models
    • CIME Lectures, Springer
    • Méléard S. Asymptotic behaviour of some interacting particle systems, McKean-Vlasov and Boltzmann models. CIME Lectures. Lecture Notes in Mathematics vol. 1627 (1996), Springer 45-95
    • (1996) Lecture Notes in Mathematics , vol.1627 , pp. 45-95
    • Méléard, S.1
  • 18
    • 0017451407 scopus 로고
    • The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk
    • Milinazzo F., and Saffman P.G. The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk. J. Comput. Phys. 23 (1977) 380-392
    • (1977) J. Comput. Phys. , vol.23 , pp. 380-392
    • Milinazzo, F.1    Saffman, P.G.2
  • 19
    • 37249045153 scopus 로고    scopus 로고
    • G. Nason, A. Kovac, M. Maechler, wavethresh R-package, http://cran.r-project.org/src/contrib/Descriptions/wavethresh.html
  • 20
    • 0001105004 scopus 로고
    • Topics in propagation of chaos
    • Ecole d'Ete de Probabilités de Saint-Flour XIX, Springer, Berlin
    • Sznitman A.S. Topics in propagation of chaos. Ecole d'Ete de Probabilités de Saint-Flour XIX. Lecture Notes in Mathematics vol. 1464 (1991), Springer, Berlin 165-251
    • (1991) Lecture Notes in Mathematics , vol.1464 , pp. 165-251
    • Sznitman, A.S.1
  • 21
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving stochastic differential equations
    • Talay D., and Tubaro L. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 4 (1990) 94-120
    • (1990) Stochastic Anal. Appl. , vol.8 , Issue.4 , pp. 94-120
    • Talay, D.1    Tubaro, L.2
  • 22
    • 0037274421 scopus 로고    scopus 로고
    • A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations
    • Talay D., and Vaillant O. A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Anal. Appl. Probab. 13 1 (2003) 140-180
    • (2003) Anal. Appl. Probab. , vol.13 , Issue.1 , pp. 140-180
    • Talay, D.1    Vaillant, O.2
  • 23
    • 37249043897 scopus 로고    scopus 로고
    • V.C. Tran, Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques. Ph.D. Thesis, Université Paris X - Nanterre, http://tel.archives-ouvertes.fr/tel-00125100
  • 24
    • 37249002473 scopus 로고    scopus 로고
    • O. Vaillant, Une méthode particulaire stochastique à poids aléatoires pour l'approximation de solutions statistiques d'équations de McKean-Vlasov-Fokker-Planck. Ph.D. Thesis, Université de Provence, Marseille, France, 2000
  • 25
    • 0003897397 scopus 로고
    • Mathematical problems of statistical hydromechanics
    • Kluwer Academic Publishers
    • Vishik M.J., and Fursikov A.V. Mathematical problems of statistical hydromechanics. Mathematics and its Applications (1980), Kluwer Academic Publishers
    • (1980) Mathematics and its Applications
    • Vishik, M.J.1    Fursikov, A.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.