Calculating Principal Eigen-Functions of Non-Negative Integral Kernels: Particle Approximations and Applications

Nick Whiteley () and Nikolas Kantas ()
Additional contact information
Nick Whiteley: School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
Nikolas Kantas: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

Mathematics of Operations Research, 2017, vol. 42, issue 4, 1007-1034

Abstract: Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigenfunction and eigenvalue of a nonnegative integral kernel. Except in the finite-dimensional case, usually neither the principal eigenfunction nor the eigenvalue can be computed exactly. In this paper, we develop numerical approximations for these quantities. We show how a generic interacting particle algorithm can be used to deliver numerical approximations of the eigenquantities and the associated so-called “twisted” Markov kernel as well as how these approximations are relevant to the aforementioned applications. In addition, we study a collection of random integral operators underlying the algorithm, address some of their mean and pathwise properties, and obtain error estimates. Finally, numerical examples are provided in the context of importance sampling for computing tail probabilities of Markov chains and computing value functions for a class of stochastic optimal control problems.

Keywords: interacting particle methods; eigenfunctions; rare events estimation; optimal control; diffusion Monte Carlo (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1287/moor.2016.0834 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:42:y:2017:i:4:p:1007-1034

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().