Exponential stability for nonlinear filtering
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 6, pp. 697-725. 
@article{AIHPB_1997__33_6_697_0,
     author = {Atar, Rami and Zeitouni, Ofer},
     title = {Exponential stability for nonlinear filtering},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {697--725},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {6},
     year = {1997},
     mrnumber = {1484538},
     zbl = {0888.93057},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1997__33_6_697_0/}
}
TY  - JOUR
AU  - Atar, Rami
AU  - Zeitouni, Ofer
TI  - Exponential stability for nonlinear filtering
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1997
SP  - 697
EP  - 725
VL  - 33
IS  - 6
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1997__33_6_697_0/
LA  - en
ID  - AIHPB_1997__33_6_697_0
ER  - 
%0 Journal Article
%A Atar, Rami
%A Zeitouni, Ofer
%T Exponential stability for nonlinear filtering
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1997
%P 697-725
%V 33
%N 6
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1997__33_6_697_0/
%G en
%F AIHPB_1997__33_6_697_0
Atar, Rami; Zeitouni, Ofer. Exponential stability for nonlinear filtering. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 6, pp. 697-725. http://www.numdam.org/item/AIHPB_1997__33_6_697_0/

[1] R. Atar and O. Zeitouni, Lyapunov Exponents for Finite State Nonlinear Filtering, Siam J. Contr. Optim., Vol. 35, No 1, 1997, pp. 36-55. | MR | Zbl

[2] G. Birkhoff, Extensions of Jentzsch's Theorem, Trans. Am. Math. Soc., Vol. 85, 1957, pp. 219-227. | MR | Zbl

[3] G. Birkhoff, Lattice Theory, Am. Math. Soc. Publ. 25, 3rd ed., 1967. | Zbl

[4] P. Bougerol, Théorèmes limites pour les systèmes linéaires à coefficients markoviens, Prob. Theory Rel. Fields, Vol. 78, 1988, pp. 192-221. | MR | Zbl

[5] P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Schrödinger Operators, Birkhäuser, 1985. | MR | Zbl

[6] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR | Zbl

[7] B. Delyon and O. Zeitouni, Lyapunov exponents for filtering problems, Applied Stochastic Analysis, edited by Davis, M. H. A. and Elliot, R. J., Gordon and Breach Science Publishers, London, pp. 511-521, 1991. | MR | Zbl

[8] F. Flandoli and K. Schaumlöffel, Stochastic Parabolic Equations in Bounded Domains: Random Evolution Operator and Lyapunov Exponents, Stochastics and Stochastic Reports, Vol. 29, 1990, pp. 461-485. | MR | Zbl

[9] E. Hopf, An Inequality for Positive Linear Integral Operators, Journal of Mathematics and Mechanics, Vol. 12, No. 5, 1963, pp. 683-692. | MR | Zbl

[10] I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, 1991. | MR | Zbl

[11] S. Karlin, Total Positivity, Stanford University Press, Stanford, California, 1968. | MR | Zbl

[12] H. Kunita, Asymptotic Behavior of the Nonlinear Filtering Errors of Markov Processes, J. Multivariate Anal., Vol. 1, 1971, pp. 365-393. | MR | Zbl

[13] R.S. Liptser and A.N. Shiryayev, A. N. Statistics of Random Processes, Nauka, Moscow, 1974, English ed., Springer-Verlag, New-york, 1977.

[14] D. Ocone and E. Pardoux, Asymptotic Stability of the Optimal Filter with respect to its Initial Condition, Siam J. Contr. Optim., Vol. 34, No. 1, 1996, pp. 226-243. | MR | Zbl

[15] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York and London, 1967. | MR | Zbl

[16] Y. Peres, Domains of Analytic Continuation for the Top Lyapunov Exponent, Ann. Inst. Henri Poincaré, Vol. 28, 1992, No. 1, pp. 131-148. | Numdam | MR | Zbl

[17] E. Seneta, Non-negative Matrices and Markov Chains, Springer-Verlag, 1981. | Zbl

[18] L. Stettner, On Invariant Measures of Filtering Processes, Stochastic Differential Systems, Proc. 4th Bad Honnef Conf., 1988, Lecture Notes in Control and Inform. Sci. 126, edited by Christopeit, N., Helmes, K. and Kohlmann, M., Springer, 1989, pp. 279-292. | MR | Zbl

[19] L. Stettner, Invariant Measures of the Pair: State, Approximate Filtering Process, Colloq. Math., LXII, 1991, pp. 347-351. | MR | Zbl

[20] M. Zakai, On the Optimal Filtering of Diffusion Processes, Z. Wahr. Verw. Geb., Vol. 11, 1969, pp. 230-243. | MR | Zbl

[21] O. Zeitouni and B.Z. Bobrovsky, On the Joint Nonlinear Filtering-Smoothing of Diffusion Processes, Systems & Control Letters, Vol. 7, 1986, pp. 317-321. | Zbl