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 Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . 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.
Mots clés : Feynman-Kac formula, Schrödinger operator, spectral radius, Lyapunov exponent, spectral decomposition, semigroups on a Banach space, interacting particle systems, genetic algorithms, asymptotic stability, central limit theorems
@article{PS_2003__7__171_0,
author = {Del Moral, Pierre and Miclo, L.},
title = {Particle approximations of {Lyapunov} exponents connected to {Schr\"odinger} operators and {Feynman-Kac} semigroups},
journal = {ESAIM: Probability and Statistics},
pages = {171--208},
publisher = {EDP-Sciences},
volume = {7},
year = {2003},
doi = {10.1051/ps:2003001},
zbl = {1040.81009},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2003001/}
}
TY - JOUR AU - Del Moral, Pierre AU - Miclo, L. TI - Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups JO - ESAIM: Probability and Statistics PY - 2003 SP - 171 EP - 208 VL - 7 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2003001/ DO - 10.1051/ps:2003001 LA - en ID - PS_2003__7__171_0 ER -
%0 Journal Article %A Del Moral, Pierre %A Miclo, L. %T Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups %J ESAIM: Probability and Statistics %D 2003 %P 171-208 %V 7 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2003001/ %R 10.1051/ps:2003001 %G en %F PS_2003__7__171_0
Del Moral, Pierre; Miclo, L. Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 171-208. doi : 10.1051/ps:2003001. http://www.numdam.org/articles/10.1051/ps:2003001/
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