Open Access
December 2013 Stability properties of some particle filters
Nick Whiteley
Ann. Appl. Probab. 23(6): 2500-2537 (December 2013). DOI: 10.1214/12-AAP909


Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic, relative variance associated with a particle approximation of the normalizing constant is bounded linearly in time. The conditions are demonstrated to hold for some hidden Markov models on noncompact state spaces. The particle stability results are obtained by proving $v$-norm multiplicative stability and exponential moment results for the underlying Feynman–Kac formulas.


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Nick Whiteley. "Stability properties of some particle filters." Ann. Appl. Probab. 23 (6) 2500 - 2537, December 2013.


Published: December 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1296.60098
MathSciNet: MR3127943
Digital Object Identifier: 10.1214/12-AAP909

Primary: 60G35 , 60K35

Keywords: Hidden Markov model , particle filter , sequential Monte Carlo

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 6 • December 2013
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