Abstract
We consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein-Uhlenbeck process with fast reversion to a shifting-mean that is controlled by a continuous time Markov chain modeling regime change. We show that the nonlinear filter for such a process can be approximated by an averaged filter that asymptotically coincides with the true nonlinear filter of the regime-changing Markov chain as the rate of mean-reversion approaches infinity. The asymptotics exploit weak convergence of the state variables to an invariant distribution, which is significantly different from the strong convergence used to obtain asymptotic results in [A. Papanicolaou, Asymptot. Anal., 70 (2010), pp. 155-176].
Original language | English (US) |
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Pages (from-to) | 906-935 |
Number of pages | 30 |
Journal | Multiscale Modeling and Simulation |
Volume | 10 |
Issue number | 3 |
DOIs | |
State | Published - 2012 |
Keywords
- Ergodic theory
- Filtering
- Hidden Markov models
- Homogenization
ASJC Scopus subject areas
- General Chemistry
- Modeling and Simulation
- Ecological Modeling
- General Physics and Astronomy
- Computer Science Applications