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 $N$ 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.

Keywords: 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, Volume 7 (2003), pp. 171-208. doi : 10.1051/ps:2003001. http://www.numdam.org/articles/10.1051/ps:2003001/

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