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A Continuous Time Particle Filter

  • Alan Bain
  • Dan Crisan
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 60)

Abstract

Throughout this chapter, we take the signal X to be the solution of (3.9); that is, \( X = ({X^i})_{i = 1}^d \) is the solution of the stochastic differential equation
$$ {d}{{X}_{t}}=f({{X}_{t}})\text{d}t+\sigma ({{X}_{t}})\text{d}{{V}_{t}}\text{, } $$
(9.1)
where f : ℝ d → ℝ d and σ : ℝ d → ℝ d×p are bounded and globally Lipschitz functions and \( V\, = \,({V^j})_{j = 1}^p \) is a p-dimensional Brownian motion.

Keywords

Minimal Variance Convergence Result Particle Approximation Martingale Property Zakai Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alan Bain
    • 1
  • Dan Crisan
    • 2
  1. 1.BNP Paribas 10 Harewood AvLondonUnited Kingdom
  2. 2.Department of MathematicsImperial College London 180 Queen’s GateLondonUnited Kingdom

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