On the stability of nonlinear Feynman-Kac semigroups

@article{Moral2002OnTS,
  title={On the stability of nonlinear Feynman-Kac semigroups},
  author={Pierre Del Moral and Laurent Miclo},
  journal={Annales de la Facult{\'e} des Sciences de Toulouse},
  year={2002},
  volume={11},
  pages={135-175}
}
  • P. MoralL. Miclo
  • Published 2002
  • Mathematics
  • Annales de la Faculté des Sciences de Toulouse
On s'interesse aux proprietes de stabilite de certains semi-groupes non-lineaires, de type Feynman-Kac renormalises, agissant sur l'ensemble des probabilites d'un espace mesure donne. Cette etude se base notamment sur l'utilisation du coefficient ergodique de Dobrushin dans l'esprit d'articles precedents de A. Guionnet et de l'un des auteurs. La seconde partie de ce travail porte sur des applications des resultats obtenus. Tout d'abord nous donnons des criteres assurant qu'une particule sous… 

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References

SHOWING 1-10 OF 15 REFERENCES

Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

This paper focuses on interacting particle systems methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology,

Entropic convergence for solutions of the Boltzmann equation with general physical initial data

Abstract We show, for a particular collision kernel, that the entropy tends to its equilibrium limit for all solutions of the spatially homogeneous Boltzmann equation with finite energy, finite

A Robust Discrete State Approximation to the Optimal Nonlinear Filter for a Diffusion.

The approximation is robust in the sense that it is locally Lipschitz continuous in the data y( °) (sup norm) uniformly in h and it converges to the optimal filter for the diffusion.

Heat kernels and spectral theory

Preface 1. Introductory concepts 2. Logarithmic Sobolev inequalities 3. Gaussian bounds on heat kernels 4. Boundary behaviour 5. Riemannian manifolds References Notation index Index.

Central Limit Theorem for Nonstationary Markov Chains. II

The second part of this paper contains proofs of results published in the first part (see the first number of this journal).

P.) & MICLO (L.)

  • 2000

Propagation of Smoothness and the Rate of Exponential Convergence to Equilibrium for a Spatially Homogeneous Maxwellian Gas

Abstract:We prove an inequality for the gain term in the Boltzmann equation for Maxwellian molecules that implies a uniform bound on Sobolev norms of the solution, provided the initial data has a

Stochastic partial differential equations that arise in nonlinear filtering problem

  • 1972

Characterization and Convergence, Wiley series in probability and mathematical statistics

  • Markov Processes
  • 1986