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Asymptotic error distributions of the Euler method for continuous-time nonlinear filtering

Japan Journal of Industrial and Applied Mathematics volume 37, pages 383–413 (2020)Cite this article

Abstract

In this paper, we deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. As studied in previous works by several authors, the error structure of the method is characterized by conditional expectations of some functionals of multiple stochastic integrals. Our main result is to prove the stable convergence of a sequence of such conditional expectations by using the techniques of martingale limit theorems in the spirit of Jacod (On continuous conditional Gaussian martingales and stable convergence in law, seminaire de probabilites, XXXI, lecture notes in mathematics, Springer, Berlin, 1997).

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo, 113-8656, Japan

    Teppei Ogihara

  2. National Institute of Technology, Toba College, 1-1 Ikegami-cho, Toba, Mie, 517-8501, Japan

    Hideyuki Tanaka

Authors
  1. Teppei Ogihara
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  2. Hideyuki Tanaka
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Correspondence to Hideyuki Tanaka.

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Ogihara, T., Tanaka, H. Asymptotic error distributions of the Euler method for continuous-time nonlinear filtering. Japan J. Indust. Appl. Math. 37, 383–413 (2020). https://doi.org/10.1007/s13160-020-00411-5

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  • DOI: https://doi.org/10.1007/s13160-020-00411-5

Keywords

  • Nonlinear filtering
  • Euler method
  • Stable convergence
  • Martingale limit theorem

Mathematics Subject Classification

  • 60G35
  • 93E11
  • 60F05
  • 65C20