Hu, Ze-Chun and Sun, Wei
A Note on Exponential Stability of the NonLinera Filter for Denumerable Markov Chains.
Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
We study asymptotic stability of the optimal filter with respect to its initial conditions. We show that exponential stability of the nonlinear filter holds for a large class of denumerable Markov chains, including all finite Markov chains, under the assumption that the observation function is one-to-one and the observation noise is sufficiently small. Ergodicity of the signal process is not assumed.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Hu, Ze-Chun and Sun, Wei|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 3/06|
Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Nonlinear filtering; exponential stability; denumerable Markov chain|
|Deposited On:||03 Jun 2010 20:04|
|Last Modified:||04 Nov 2016 22:58|
References:Atar R., 1998. Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain. Ann. Prob. 26 (4), 1552-1574.
Atar R., Zeitouni O., 1997a. Lyapunov exponents for finite state nonlinear filtering. SIAM J. Control Optim. 35 (1), 36-55.
Atar R., Zeitouni O., 1997b. Exponential stability for nonlinear filtering. Ann. Inst. H. Poincaré Prob. Stat. 33 (6), 697-725.
Baxendale P., Chigansky P., Liptser R., 2004. Asymptotic stability of the Wonham filter: ergodic and nonergodic signals. SIAM J. Control Optim. 43 (2), 643-669.
Budhiraja A., 2003. Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter. Ann. Inst. H. Poincar´e Prob. Stat. 39 (6), 919–941.
Budhiraja A., Ocone D. L., 1999. Exponential stability of discrete-time filters for non-ergodic signals. Stochastic Process. Appl. 82 (2), 245-257.
Chigansky P., 2005. On exponential stability of the nonlinear filter for slowly switching Markov chains. Preprint.
Chigansky P., Liptser R., 2004. Stability of nonlinear filters in nonmixing case. Ann. Appl. Prob. 14 (4), 2038-2056.
Del Moral P., Guionnet A., 2001. On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. H. Poincaré Prob. Stat. 37 (2), 155-194.
Kaijser T., 1975. A limit theorem for partially observed Markov chains. Ann. Prob. 3 (4), 677-696.
Kunita H., 1971. Asymptotic behavior of the nonlinear filtering errors of Markov processes. J. Multivariate Anal. 1, 365-393.
LeGland F., Oudjane N., 2003. A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals. Stochastic Process. Appl. 106 (2), 279-316.
Ocone D., Pardoux E., 1996. Asymptotic stability of the optimal filter with respect to its initial conditions. SIAM J. Control and Optim. 34 (1), 226-243.
Stannat W., 2004a. Stability of the filter equation for a time-dependent signal on Rd. Appl. Math. Optim. 52 (1), 39-71.
Stannat W., 2004b. Stability of the pathwise filter equation on Rd. Preprint.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access
Repository Staff Only: item control page