Counting Observations: A Note on State Estimation Sensitivity with an L
1
-Bound |
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Authors: | A Calzolari G Nappo |
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Institution: | (1) Dipartimento di Matematica, Università di Roma ``Tor Vergata,' Via della Ricerca Scientifica, 00133 Roma, Italia , IT;(2) Dipartimento di Matematica, Università di Roma ``La Sapienza,' Piazzale Aldo Moro 2, 00185 Roma, Italia , IT |
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Abstract: | Let (X
t
, Y
t
) be a pure jump Markov process: the state X
t
takes real values and the observation Y
t
is a counting process. The two processes are allowed to have common jump times. Let ϕ(X(⋅)) be a functional of the state trajectory restricted to the time interval 0, T] . If we change the infinitesimal parameters and/ or the initial distribution, then we introduce an error in computing the conditional law of ϕ(X(⋅)) given the observation up to time T . In this paper we give an explicit L
1
-bound for this error.
Accepted 9 March 2001. Online publication 20 June 2001. |
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Keywords: | , Jump processes, Counting processes, Coupling, Robustness, Filtering, Smoothing, AMS Classification, 60G35, 70J75,,,,,,93E11, 62G35, 62M20, |
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