A Continuous Time Particle Filter

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


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
$$ {d}{{X}_{t}}=f({{X}_{t}})\text{d}t+\sigma ({{X}_{t}})\text{d}{{V}_{t}}\text{, } $$
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.


Minimal Variance Convergence Result Particle Approximation Martingale Property Zakai Equation 
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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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