On conditional McKean Lagrangian stochastic models

Probability Theory and Related Fields

Volumn 151, Issue 1, 2011, Pages 319-351

  Bossy, Mireille ^a   Jabir, Jean François ^b   Talay, Denis ^a  

^a INRIA   (France)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

Conditional McKean nonlinearity; Lagrangian stochastic model

Indexed keywords

EID: 80052820894     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-010-0301-z     Document Type: Article

References (19)

1. Amann, H.: Linear and quasilinear parabolic problems. Vol. I. In: Monographs in Mathematics, vol. 89. Birkhäuser, Boston (1995).
2. Bernardin F., Bossy M., Chauvin C., Drobinski P., Rousseau A., Salameh T.: Stochastic downscaling methods: application to wind refinement. Stoch. Environ. Res. Risk Assess. 23(6), 851-859 (2009).
3. Bossy, M., Jabir, J.-F.: Confined Langevin systems for the mean no-permeability conditions (2010, preprint).
4. Dermoune A.: Propagation and conditional propagation of chaos for pressureless gas equations. Probab. Theory Relat. Fields 126(4), 459-476 (2003).
5. Di Francesco M., Pascucci A.: On a class of degenerate parabolic equations of Kolmogorov type. AMRX Appl. Math. Res. Express 3, 77-116 (2005).
6. Di Francesco M., Polidoro S.: Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form. Adv. Differ. Equ. 11(11), 1261-1320 (2006).
7. Dreeben T. D., Pope S. B.: Wall-function treatment in pdf methods for turbulent flows. Phys. Fluids 9, 2692-2703 (1997).
8. Henry D.: Geometric Theory of Semilinear Parabolic Equations. Springer, Berlin (1981).
9. Jabir, J.-F.: Modèles Stochastiques Lagrangiens de Type McKean-Vlasov Conditionnel et Leur Confinement. Ph. D. thesis, University of Nice Sophia Antipolis (2008).
10. Méléard S., Roelly-Coppoletta S.: A propagation of chaos result for a system of particles with moderate interaction. Stoch. Process. Appl. 26(2), 317-332 (1987).
11. Mohammadi B., Pironneau O.: Analysis of the k - ε Turbulence Model. Masson, Paris (1995).
12. Oelschläger K.: A law of large numbers for moderately interacting diffusion processes. Z. Wahrsch. Verw. Gebiete 69(2), 279-322 (1985).
13. Pope S. B.: On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys. Fluids 6, 973-985 (1994).
14. Pope S. B.: Turbulent Flows. Cambridge University Press, London (2003).
15. Pope S. B., Xu J.: Assessment of numerical accuracy of pdf/Monte-Carlo methods for turbulent reacting flows. J. Comput. Phys. 152, 192-230 (1999).
16. Rana I. K.: An Introduction to Measure and Integration, 2nd edn. American Mathematical Society, Providence (2002).
17. Stroock D. W., Varadhan S. R. S.: Multidimensional Diffusion Processes, vol. 233. Springer, Berlin (1979).
18. Sznitman A.-S.: A propagation of chaos result for Burgers' equation. Probab. Theory Relat. Fields 71(4), 581-613 (1986).
19. Sznitman, A.-S.: Topics in propagation of chaos. In: École d'Été de Probabilités de Saint-Flour XIX-1989. Lecture Notes in Mathematics, vol. 1464. Springer, Berlin (1991).