Robust approximation in a filtering problem with real state space and counting observations

Applied Mathematics and Optimization

Volumn 42, Issue 1, 2000, Pages 51-71

  Calzolari, A ^a   Nappo, G ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MARKOV PROCESSES; STATE SPACE METHODS;

JUMP MARKOV PROCESS;

NONLINEAR FILTERING;

EID: 0033704203     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002450010002     Document Type: Article

References (16)

1. E. Arjas, G. Nappo (1997), A note on sensitivity for intensity function estimation of a Poisson process. Unpublished manuscript.
2. R. Atar, F. Viens, O. Zeitouni (1998), Robustness of Zakai's equation via Feynman-Kac representations. Preprint.
3. R. Atar, O. Zeitouni (1997), Exponential stability for nonlinear filtering. Ann. Inst. H. Poincaré, 33(6):697-725.
4. P. Brémaud (1981), Point Processes and Queues: Martingales Dynamics. Springer-Verlag, New York.
5. A. Budhiraja, G. Kallianpur (1997), The Feynman-Stratonovich Semigroup and Stratonovich Integral Expansions in Nonlinear Filtering. Appl. Math. Optim., 35:91-116.
6. A. Budhiraja, H. J. Kushner (1998), Robustness of nonlinear filters over the infinite time interval. SIAM J. Control Optim., 36(5): 1618-1637.
7. A. Budhiraja, D. Ocone (1997), Exponential stability of discrete-time filters for bounded observation noise. System Control Lett., 30:185-193.
8. A. Calzolari, G. Nappo (1996), A filtering problem with counting observation: approximation with error bounds. Stochastics Stochastics Rep., 57:71-87.
9. A. Calzolari, G. Nappo (1997), A filtering problem with counting observation: error bounds due to the uncertainty on the infinitesimal parameters. Stochastics Stochastics Rep., 61:1-19.
10. 1-bound. Internal note 97/46, Dip. Mat. "G. Castelnuovo," Univ. Roma "La Sapienza."
11. P.J. Huber (1981), Robust Statistics. Wiley, New York.
12. W. H. Kliemann, G. Koch, F. Marchetti (1990), On the unnormalized solution of the filtering problem with counting process observations. IEEE Trans. Inform. Theory, 36(6):1415-1425.
13. H. Korezlioglu, W. J. Runggaldier (1993), Filtering for nonlinear systems driven by nonwhite noises: an approximation scheme. Stochastics, 44:65-102.
14. H. J. Kushner (1979), A robust computable approximation to the optimal nonlinear filter. Stochastics, 3:75-83.
15. D. Ocone, E. Pardoux (1996), Asymptotic stability of the optimal filter with respect to its initial conditions. SIAM J. Control Optim., 34(1):226-243.
16. S. T. Rachev (1991), Probability metrics and the stability of stochastic models. Wiley, New York.