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Article Dans Une Revue Communications in Statistics - Theory and Methods Année : 2007

Filtering and the EM-algorithm for the Markovian arrival process

Résumé

In this article, we deal with the so-called Markovian Arrival Process (MAP). An MAP is thought of as a partially observed Markov process, so that the Expectation-Maximization (EM) algorithm is a natural way to estimate its parameters. Then, nonlinear filters of basic statistics related to the MAP must be computed. The forward-backward principle is the basic way to do it. Here, bearing in mind a filter-based formulation of the EM-algorithm proposed by Elliott, these filters are shown to be the solution of nonlinear stochastic differential equations (SDEs) which allows a recursive computation. This is well suited for processing large data sets. We also derive linear SDEs or Zakai equations for the so-called unnormalized filters
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Dates et versions

hal-00368486 , version 1 (19-08-2013)

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James Ledoux. Filtering and the EM-algorithm for the Markovian arrival process. Communications in Statistics - Theory and Methods, 2007, 36 (14), pp.2577-2593. ⟨10.1080/03610920701271038⟩. ⟨hal-00368486⟩
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