Imperial College London
Alternate

Dr Nikolas Kantas

Faculty of Natural Sciences, Department of Mathematics

Reader in Statistics
 
 
 
//

Contact

 

+44 (0)20 7594 2772n.kantas Website

 
 
//

Location

 

538Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Whiteley:2012:10.1016/j.spa.2012.02.002,
author = {Whiteley, N and Kantas, N and Jasra, A},
doi = {10.1016/j.spa.2012.02.002},
journal = {Stochastic Processes and their Applications},
title = {Linear Variance Bounds for Particle Approximations of Time-Homogeneous  Feynman-Kac Formulae},
url = {http://dx.doi.org/10.1016/j.spa.2012.02.002},
year = {2012}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This article establishes sufficient conditions for a linear-in-time bound onthe non-asymptotic variance of particle approximations of time-homogeneousFeynman-Kac formulae. These formulae appear in a wide variety of applicationsincluding option pricing in finance and risk sensitive control in engineering.In direct Monte Carlo approximation of these formulae, the non-asymptoticvariance typically increases at an exponential rate in the time parameter. Itis shown that a linear bound holds when a non-negative kernel, defined by thelogarithmic potential function and Markov kernel which specify the Feynman-Kacmodel, satisfies a type of multiplicative drift condition and other regularityassumptions. Examples illustrate that these conditions are general and flexibleenough to accommodate two rather extreme cases, which can occur in the contextof a non-compact state space: 1) when the potential function is bounded above,not bounded below and the Markov kernel is not ergodic; and 2) when thepotential function is not bounded above, but the Markov kernel itself satisfiesa multiplicative drift condition.
AU  - Whiteley,N
AU  - Kantas,N
AU  - Jasra,A
DO  - 10.1016/j.spa.2012.02.002
PY  - 2012///
TI  - Linear Variance Bounds for Particle Approximations of Time-Homogeneous  Feynman-Kac Formulae
T2  - Stochastic Processes and their Applications
UR  - http://dx.doi.org/10.1016/j.spa.2012.02.002
UR  - http://arxiv.org/abs/1108.3988v2
UR  - http://hdl.handle.net/10044/1/18636
ER  -
Download