Kouritzin, Michael A. and Sun, Wei (2004) Rates for Branching Particle Approximations of ContinuousDiscrete 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 continuousdiscrete filtering problems. Suppose that t → Xt is a Markov process and we wish to calculate the measurevalued 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 observationdependent 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 Lévystable signals and give rates of convergence for E1/2[µnt  µt2√], ∙ √ 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 16:20 
Last Modified:  08 Dec 2010 23:24 
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