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@article{Whiteley:2017:10.1287/moor.2016.0834,
author = {Whiteley, N and Kantas, N},
doi = {10.1287/moor.2016.0834},
journal = {Mathematics of Operations Research},
pages = {1007--1034},
title = {Calculating principal eigen-functions of non-negative integral kernels:  particle approximations and applications},
url = {http://dx.doi.org/10.1287/moor.2016.0834},
volume = {42},
year = {2017}
}

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TY  - JOUR
AB  - Often in applications such as rare events estimation or optimal control it isrequired that one calculates the principal eigen-function and eigen-value of anon-negative integral kernel. Except in the finite-dimensional case, usuallyneither the principal eigen-function nor the eigen-value can be computedexactly. In this paper, we develop numerical approximations for thesequantities. We show how a generic interacting particle algorithm can be used todeliver numerical approximations of the eigen-quantities and the associatedso-called "twisted" Markov kernel as well as how these approximations arerelevant to the aforementioned applications. In addition, we study a collectionof random integral operators underlying the algorithm, address some of theirmean and path-wise properties, and obtain $L_{r}$ error estimates. Finally,numerical examples are provided in the context of importance sampling forcomputing tail probabilities of Markov chains and computing value functions fora class of stochastic optimal control problems.
AU  - Whiteley,N
AU  - Kantas,N
DO  - 10.1287/moor.2016.0834
EP  - 1034
PY  - 2017///
SN  - 1526-5471
SP  - 1007
TI  - Calculating principal eigen-functions of non-negative integral kernels:  particle approximations and applications
T2  - Mathematics of Operations Research
UR  - http://dx.doi.org/10.1287/moor.2016.0834
UR  - http://hdl.handle.net/10044/1/40800
VL  - 42
ER  -

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Dr Nikolas Kantas

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