Warianty tytułu
Języki publikacji
Abstrakty
The paper describes briefly a history of filtering problems of Markov processes and then concentrates on ergodic properties of filtering process. A mistake in a famous Kunita paper on ergodicity of filtering processes is shown. Then the paper reviews various attempts trying to correct this mistake. (original abstract)
Słowa kluczowe
Twórcy
autor
- Polish Academy of Sciences, Poland
Bibliografia
- Atar R., Zeitouni O., Lyapunov exponents for finite-state nonlinear filtering, SIAM J. Control Optim. 35 (1997), 36-55.
- Baxendale P., Chigansky P., Liptser R., Asymptotic stability of the Wonham filter: ergodic and nonergodic signals, Preprint 2002.
- Borkar V.S., Ergodic control of partially observed Markov chains, Systems Control Lett. 34 (1998), 185-189.
- Borkar V.S., Budhiraja A., A further remark on dynamic programming for partially observed Markov processes, Stochastic Process. Appl. 112 (2004), 79-93.
- Di Masi G., Stettner L., Ergodicity of Hidden Markov Models, Math. Control Signals Systems 17 (2005), 269-296.
- Di Masi G., Stettner L., Ergodicity of filtering process by vanishing discount approach, Systems Control Lett. 57 (2008), 150-157.
- Di Masi G., Stettner L., Risk sensitive control of discrete time partially observed Markov processes with infinite horizon, Stochastics and Stochastics Rep. 67 (1999), 309-322.
- Ikeda N., Watanabe Sh., Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
- Kaijser T., A limit theorem for partially observed Markov chains, Ann. Probab. 3 (1975), 677-696.
- Kakutani S., Ergodic theorems and the Markoff processes with a stable distribution, Proc. Imp. Acad. Tokyo 16 (1940), 49-54.
- Kallenberg O., Foundations of Modern Probability, Springer-Verlag, New York-Berlin, 1997.
- Kunita H., Asymptotic behaviour of the nonlinear filtering errors of Markov process, J. Multivariate Anal. 1 (1971), 365-393.
- Kunita H., Ergodic properties of nonlinear filtering processes , in: Spatial Stochastic Processes, ed. by Aleksander K.C., Watkins J.C., Progr. Probab. 19 , Birkhauser, Boston, 1991, pp. 233-256.
- Liptser R., Shiryaev A.N., Statistics of Random Processes II. Applications, Second Edition, Springer-Verlag, New York-Berlin, 2001.
- Liverani C., Decay of correlations, Ann. of Math. 142 (1995), 239-301.
- Meyn S.P., Tweedie R.L., Markov Chains and Stochastics Stability, Springer-Verlag, New York-Berlin, 1993.
- Ocone D., Pardoux E., Asymptotic stability of the optimal filter with respect to its initial conditions, SIAM J. Control Optim. 34 (1996), 226-243.
- Runggaldier W., Stettner L., Approximations of Discrete Time Partially Observed Control Problems, Applied Mathematics Monographs CNR, Giardini Editori, Pisa, 1994.
- Schäl M., Average Optimality in Dymanic Programming with General State Space, Math. Oper. Res. 18 (1993), 163-172.
- Stettner L., On Invariant Measures of Filtering Processes , in: Proc. 4th Bad Honnef Conf. on Stochastic Differential Systems, ed. by Christopeit N., Helmes K., Kohlmann M., Lect. Notes in Control Inf. Sci. 126, Springer-Verlag, New York-Berlin, 1989, pp. 279-292.
- Stettner L., Ergodic control of partially observed Markov processes with equivalent transition probabilities, Appl. Math. (Warsaw) 22 (1993), 25-38.
- Tong X.T., van Handel R., Ergodicity and stability of the conditional distributions of nondegenerate Markov chains, Ann. Appl. Probab. 22 (2012), 1495-1540.
- van Handel R., The stability of conditional Markov processes and Markov chains in random environments, Ann. Probab. 37 (2009), 1876-1925.
- van Handel R., A nasty filtering problem, Preprint 2010, arXiv:1009.0507.
- Yosida K., Functional Analysis, Springer-Verlag, New York-Berlin, 1978.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171621394