Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups
ESAIM: Probability and Statistics, Volume 7 (2003), p. 171-208

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.

DOI : https://doi.org/10.1051/ps:2003001
Classification:  62L20,  65C05,  81Q05,  82C22
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},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     pages = {171-208},
     doi = {10.1051/ps:2003001},
     zbl = {1040.81009},
     language = {en},
     url = {http://www.numdam.org/item/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/item/PS_2003__7__171_0/

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