Nonlinear filtering and measure-valued processes

  title={Nonlinear filtering and measure-valued processes},
  author={D. Crisan and Terry Lyons},
  journal={Probability Theory and Related Fields},
  • D. Crisan, Terry Lyons
  • Published 1997
  • Mathematics
  • Probability Theory and Related Fields
  • Summary. We construct a sequence of branching particle systems with time and space dependent branching mechanisms whose expectation converges to the solution of the Zakai equation. This gives an alternative numerical method to solve the Filtering Problem. 
    77 Citations
    Particle Approximations for a Class of Stochastic Partial Differential Equations
    • 27
    Particle representations for a class of nonlinear SPDEs
    • 147
    • PDF
    Interacting Particle Systems Approximations ofthe
    • Kushner Stratonovitch EquationD, P. Del Moraly, Terry Lyons
    • 1999
    Convergence of a Branching Particle Method to the Solution of the Zakai Equation
    • 90
    • PDF


    Approximation of nonlinear filtering problems and order of convergence
    • 43
    Markov Processes: Characterization and Convergence
    • 4,314
    • Highly Influential
    • PDF
    Convergence of Probability Measures
    • 7,963
    Stochastic Control of Partially Observable Systems
    • 536
    • Highly Influential
    Topics in Nonlinear Filtering Theory.
    • 57
    Stopping Times and Tightness. II
    • 367
    • PDF
    Sampling-Based Approaches to Calculating Marginal Densities
    • 6,664
    • PDF
    Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
    • S. Geman, D. Geman
    • Mathematics, Computer Science
    • IEEE Transactions on Pattern Analysis and Machine Intelligence
    • 1984
    • 13,290
    • PDF
    Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling
    • 983
    • PDF