We consider a pure jump Markov process (Xt Yt ) with discrete state space. We suppose that the state Xt is not observable and that the observation Yt is a counting process. We construct an approximation for the filter of Xt given (Ys s ≤ t), by means of a family of piecewise constant processes, depending on the value of Yt and on the time discretization parameter. Moreover we give an explicit error bound for the convergence of the scheme
Calzolari, A., Nappo, G. (1996). A Filtering Problem with Counting Observations: Approximations with Error Bounds. STOCHASTICS AND STOCHASTICS REPORTS, 57, 71-87 [10.1080/17442509608834052].
A Filtering Problem with Counting Observations: Approximations with Error Bounds
CALZOLARI, ANTONELLA;
1996-01-01
Abstract
We consider a pure jump Markov process (Xt Yt ) with discrete state space. We suppose that the state Xt is not observable and that the observation Yt is a counting process. We construct an approximation for the filter of Xt given (Ys s ≤ t), by means of a family of piecewise constant processes, depending on the value of Yt and on the time discretization parameter. Moreover we give an explicit error bound for the convergence of the schemeFile in questo prodotto:
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