### Abstract

We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponential decay of the derivative of the nonlinear filter with respect to its initial condition. We allow simultaneously for misspecification of the initial condition, of the transition rates of the signal, and of the observation function. The first two cases are treated by relatively elementary means, while the latter case requires the use of Skorokhod integrals and tools of anticipative stochastic calculus.

Original language | English (US) |
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Pages (from-to) | 688-715 |

Number of pages | 28 |

Journal | Annals of Applied Probability |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2007 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Keywords

- Anticipative stochastic calculus
- Error bounds
- Filter stability
- Markov chains
- Model robustness
- Nonlinear filtering