论文信息 - Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman{Kac semigroups and for estimating the principal eigenvalue of Schrodinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V. These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine a class of models extending the hard obstacle model of K. Burdzy, R. Holyst and P. March and including the Moran type scheme presented by the authors in a previous work. We provide precise uniform estimates with respect to the time parameter and we analyze the fluctuations of continuous time particle models.

Pierre Del Moral | Laurent Miclo | P. Moral | L. Miclo

[1] G. Parisi. Brownian motion , 2005, Nature.

[2] A. Sznitman. Brownian motion, obstacles, and random media , 1998 .

[3] Robert Holyst,et al. Configurational transition in a Fleming - Viot-type model and probabilistic interpretation of Laplacian eigenfunctions , 1996 .

[4] J. Doob. Stochastic processes , 1953 .

[5] Laurent Miclo,et al. A Moran particle system approximation of Feynman-Kac formulae , 2000 .

[6] P. Moral,et al. On the stability of interacting processes with applications to filtering and genetic algorithms , 2001 .

[7] A. Shiryaev,et al. Limit Theorems for Stochastic Processes , 1987 .

[8] Tosio Kato. Perturbation theory for linear operators , 1966 .

[9] P. Moral,et al. Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models , 2001 .

[10] P. Moral,et al. Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering , 2000 .

[11] Peter March,et al. A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian , 2000 .