On the LP-convergence of a Girsanov theorem based particle filter

Abstract : We analyze the L p-convergence of a previously proposed Girsanov theorem based particle filter for discretely observed stochastic differential equation (SDE) models. We prove the convergence of the algorithm with the number of particles tending to infinity by requiring a moment condition and a step-wise initial condition boundedness for the stochastic exponential process giving the likelihood ratio of the SDEs. The practical implications of the condition are illustrated with an Ornstein–Uhlenbeck model and with a non-linear Bene˘ s model.
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Submitted on : Monday, December 19, 2016 - 8:10:00 PM
Last modification on : Wednesday, December 4, 2019 - 1:34:07 PM

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Simo Särkkä, Éric Moulines. On the LP-convergence of a Girsanov theorem based particle filter. ICASSP 2016 - International Conference on Acoustics, Speech and Signal Processing , Mar 2016, Shangai, China. pp.3989 - 3993, ⟨10.1109/ICASSP.2016.7472426⟩. ⟨hal-01419046⟩

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