Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter

Bernoulli

Volumn 10, Issue 4, 2004, Pages 701-720

  Genon Catalot, Valentine ^a   Kessler, Mathieu ^b  

^a CNRS   (France)

^b TECHNICAL UNIVERSITY OF CARTAGENA   (Spain)

Author keywords

Discrete time observations; Filtering; Hidden Markov models; Multiplicative noise; Stability of the filtering algorithm

Indexed keywords

EID: 30344458333     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1093265637     Document Type: Article

References (7)

1. Bougerol, P. (1993) Kalman filtering with random coefficients and contractions. SIAM. J. Control Optim., 31, 942-959.
2. Del Moral, P. and Guionnet, A. (2001) On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. H. Poincaré Probab. Statist., 37(2), 155-194.
3. Elliott, R.J., Lakhdar, A. and Moore, J.B. (1995) Hidden Markov Models: Estimation and Control. Berlin: Springer-Verlag.
4. Genon-Catalot, V. (2003) A non-linear explicity filter. Statist. Probab. Lett., 61, 145-154.
5. Runggaldier, W.J. and Spizzichino, F. (2001) Sufficient conditions for finite dimensionality for filters in discrete time: a Laplace transform-based approach. Bernoulli, 7, 211-221.
6. Sawitzki, G. (1981) Finite-dimensional filters in discrete time. Stochastics 5, 107-114.
7. Yger, A. (2001) Analyse complexe et distributions: cours et exercices corrigés. Paris: Ellipses.