A particle approximation of the solution of the Kushner–Stratonovitch equation

@article{Crisan1998APA,
  title={A particle approximation of the solution of the Kushner–Stratonovitch equation},
  author={D. Crisan and Terry Lyons},
  journal={Probability Theory and Related Fields},
  year={1998},
  volume={115},
  pages={549-578}
}
  • D. Crisan, Terry Lyons
  • Published 1998
  • Mathematics
  • Probability Theory and Related Fields
  • Abstract. We construct a sequence of branching particle systems αn convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n¼. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far. 
    Convergence of a Branching Particle Method to the Solution of the Zakai Equation
    • 89
    • PDF
    Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering
    • 265
    • Highly Influenced
    • PDF
    Numerical solutions for a class of SPDEs over bounded domains
    • 6
    • PDF
    Discretization and Simulation of the Zakai Equation
    • 36
    • PDF
    An Ensemble Kushner-Stratonovich-Poisson Filter for Recursive Estimation in Nonlinear Dynamical Systems
    • 5
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 10 REFERENCES
    Convergence of a Branching Particle Method to the Solution of the Zakai Equation
    • 89
    • PDF
    Nonlinear filtering and measure-valued processes
    • 75
    Nonlinear Filtering Using Random Particles
    • 71
    Stopping Times and Tightness. II
    • 361
    • PDF
    Stochastic Control of Partially Observable Systems
    • 532
    • Highly Influential
    Monte Carlo Method for Nonlinear Filtering
    • 4