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A Moran particle system approximation of Feynman-Kac formulae

Author

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  • Moral, P. Del
  • Miclo, L.

Abstract

We present a weighted sampling Moran particle system model for the numerical solving of a class of Feynman-Kac formulae which arise in different fields. Our major motivation was from nonlinear filtering, but our approach is context free. We will show that under certain regularity conditions the resulting interacting particle scheme converges to the considered nonlinear equations. In the setting of nonlinear filtering, the -convergence exponent resulting from our proof also improves recent results on other particle interpretations of these equations.

Suggested Citation

  • Moral, P. Del & Miclo, L., 2000. "A Moran particle system approximation of Feynman-Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 193-216, April.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:2:p:193-216
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    Cited by:

    1. Angeli, Letizia & Grosskinsky, Stefan & Johansen, Adam M., 2021. "Limit theorems for cloning algorithms," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 117-152.
    2. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts & Andrew Stuart, 2010. "Random‐weight particle filtering of continuous time processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 497-512, September.
    3. Corujo, Josué, 2021. "Dynamics of a Fleming–Viot type particle system on the cycle graph," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 57-91.
    4. Cloez, Bertrand & Thai, Marie-Noémie, 2016. "Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 680-702.
    5. Cloez, Bertrand & Corujo, Josué, 2022. "Uniform in time propagation of chaos for a Moran model," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 251-285.

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