@article{AFST_2002_6_11_2_135_0, author = {Pierre Del Moral and Laurent Miclo}, title = {On the stability of nonlinear {Feynman-Kac} semigroups}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {135--175}, publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences}, address = {Toulouse}, volume = {Ser. 6, 11}, number = {2}, year = {2002}, zbl = {02052899}, mrnumber = {1988460}, language = {en}, url = {https://afst.centre-mersenne.org/item/AFST_2002_6_11_2_135_0/} }
TY - JOUR AU - Pierre Del Moral AU - Laurent Miclo TI - On the stability of nonlinear Feynman-Kac semigroups JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2002 SP - 135 EP - 175 VL - 11 IS - 2 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2002_6_11_2_135_0/ LA - en ID - AFST_2002_6_11_2_135_0 ER -
%0 Journal Article %A Pierre Del Moral %A Laurent Miclo %T On the stability of nonlinear Feynman-Kac semigroups %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2002 %P 135-175 %V 11 %N 2 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2002_6_11_2_135_0/ %G en %F AFST_2002_6_11_2_135_0
Pierre Del Moral; Laurent Miclo. On the stability of nonlinear Feynman-Kac semigroups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 11 (2002) no. 2, pp. 135-175. https://afst.centre-mersenne.org/item/AFST_2002_6_11_2_135_0/
[1] L'hypercontractivité et son utilisation en théorie des semi-groupes, École d'été de St. Flour XXII-1992, Lecture Notes in Math, 1581, Ed. P. Bernard. | MR | Zbl
). -[2] Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous maxwellian gas, Comm. Math. Phys. 199 (1999), n° 3, pp. 521-546. | MR | Zbl
). -[3] Entropic convergence for solutions of the Boltzmann equation with general physical initial data, Transport Theory Statist. Phys. 26 (1997), n° 3, pp. 373-378. | Zbl
), ) & ). -[4] The design of robust approximation to stochastic differential equations of nonlinear filtering, Comm. Systems and Random Process Theory, (Ed. J.K. Skwirzinski), Sithof and Noordhoof (1978). | MR
).-[5] Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR | Zbl
). -[6] On the stability of interacting processes with applications to filtering and genetic algorithms, Ann. de l'Inst. H. Poincaré Probab. Statist., to appear (2001). | Numdam | Zbl
) & ). -[7] The Monte-Carlo Method for filtering with discrete time observations, Probability Theory and Related Fields, to appear (2001). | Zbl
), ) & ). -[8] Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering, Séminaire de Probabilités XXXIV, Lecture Notes in Mathematics, Springer, Vol. 1729 (2000), pp. 1-145. | Numdam | Zbl
) & ). -[9] About the strong propagation of chaos for interacting particle approximations of Feynman-Kac formulae, Preprint (2000).
) & ). -[10] Central limit theorem for nonstationnary Markov chains, I,II, Theory of Proba and its applications, Vol 1, number 1 and 4 (1956), pp. 66-80 and pp. 330-385. | MR | Zbl
). -[11] Markov Processes, Characterization and Convergence, Wiley series in probability and mathematical statistics, John Wiley and Sons, New York, 1986. | Zbl
) & ). -[12] Optimal control and nonlinear filtering for nondegenerate diffusion processes, Stochastics, Vol. 8 (1972), pp. 63-77. | Zbl
) & ). -[13] Limit Theorems for Stochastic Processes, Springer- Verlag, 288 (1987). | Zbl
) & ). -[14] A robust discrete state approximation to the optimal nonlinear filter for a diffusion, Stochastics, Vol. 3 (1979), pp. 75-83. | MR | Zbl
). -[15] Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models, In D. Talay and L. Tubaro, editors, Probabilistic Models for Nonlinear Partial Differential Equations, Montecatini Terme, 1995, Lecture Notes in Mathematics, 1627, Springer-Verlag, 1996. | MR | Zbl
). -[16] Équation du lissage non linéaire, de la prédiction et du lissage, Stochastics, vol. 6 (1982), pp. 193-231. | MR | Zbl
). -[17] Continuous Martingales and Brownian Motion, Springer-Verlag, 293, 2nd Ed. (1991). | Zbl
) & ). -[18] Stochastic partial differential equations that arise in nonlinear filtering problem, U.M.N. XXVII, 3 (1972), pp. 213-214. | Zbl
). -[19] Free energy and the convergence of distributions of diffusions of McKean type, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math., 34, pp. 443-484. | MR | Zbl
). -