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Rates for Branching Particle Approximations of Continuous-Discrete Filters

Title:

Rates for Branching Particle Approximations of Continuous-Discrete Filters

Kouritzin, Michael A. and Sun, Wei (2004) Rates for Branching Particle Approximations of Continuous-Discrete Filters. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

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Abstract

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t → Xt is a Markov process and we wish to calculate the measure-valued process t →µt(∙) ≐ P(Xt ∉∙|σ{Ytk , tk ≤ t}), where tk = kε and Ytk is a distorted, corrupted, partial observation of Xtk. Then, one constructs a particle system with observation-dependent branching and n initial particles whose empirical measure at time t;µnt , closely approximates µt. Each particle evolves independently of the other particles according to the law of the signal between observation times tk, and branches with small probability at an observation time. For filtering problems where ε is very small, using the algorithm considered in this paper requires far fewer computations than other algorithms that branch or interact all particles regardless of the value of ε. We analyze the algorithm on Lévy-stable signals and give rates of convergence for E1/2[||µnt - µt||2√], ||∙ ||√ is a Sobolev norm, as well as related
convergence results.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Kouritzin, Michael A. and Sun, Wei
Series Name:Department of Mathematics & Statistics. Technical Report No. 12/04
Corporate Authors:Concordia University. Department of Mathematics & Statistics
Institution:Concordia University
Date:December 2004
Keywords:Filtering, reference probability measure method, branching particle approximations, rates of convergence, Fourier analysis
ID Code:6661
Deposited By:DIANE MICHAUD
Deposited On:02 Jun 2010 12:20
Last Modified:08 Dec 2010 18:24
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