English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider filtering for a hidden Markov model that evolves with multipletime scales in the hidden states. In particular, we consider the case where oneof the states is a scaled Ornstein-Uhlenbeck process with fast reversion to ashifting-mean that is controlled by a continuous time Markov chain modelingregime change. We show that the nonlinear filter for such a process can beapproximated by an averaged filter that asymptotically coincides with the truenonlinear filter of the regime-changing Markov chain as the rate of meanreversion approaches infinity. The asymptotics exploit weak converge of thestate variables to an invariant distribution, which is significantly differentfrom the strong convergence used to obtain asymptotic results in "Filtering forFast Mean-Reverting Processes" (19).

Nonlinear Filters for Hidden Markov Models of Regime Change with Fast Mean-Reverting States