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References
H. Akaike, Statistical predictor identification, Ann. Inst. Statis. Math., 22 (1970), pp.202–217.
Arató, M., Linear Stochastic Systems with Constant Coefficients. Lecture Notes in Control and Information Science, Springer, (1984).
K.J. Åström, and B. Wittenmark, On self-tuning regulators. Automatica, 9 (1973), pp.185–199.
A. Bagchi and V. Borkar, Parameter identification in infinite-dimensional linear systems,Stochastics,12 (1984),201–213.
J. Baikovicius and L. Gerencsér, Change point detection in a stochastic complexity framework. To appear in the Proc of the 29-th IEEE CDC, Vol 6, (1990), 3554–3555.
A. Benveniste, M. Metivier, and P. Priouret, Algorithms adaptatifs et approximations stochastiques, Masson, Paris, (1987).
A.N. Borodin, A stochastic approximation procedure in the case of weakly dependent observations, Theory Probab. Appl, 24 (1979), 34–52.
P.E. Caines, Linear Stochastic Systems, Wiley, (1988).
H.F. Chen,Recursive Estimation and Control for Stochastic Systems, John Wiley & Sons, New York, (1985).
M.H.A. Davis and R.B. Vinter, Stochastics Modelling and Control, Chapman and Hall, New York, (1985).
L.D. Davisson, Prediction error of stationary Gaussian time series of unknown covariance, IEEE Trans. Inform. Theory, IT-19 (1965), pp.783–795.
M. Deistler and B.D.O. Anderson, Linear dynamic errors-in-variable models. Some structure theory. J. of Econometrics, 41 (1989), pp.39–63,.
D.P. Djereveckii and A.L. Fradko, Applied theory of discrete adaptive control systems, (In Russian), Nauka, Moscow (1981).
T.E. Duncan, and B. Pasik-Duncan, Adaptive Control of Continuous-Time Linear Stochastic Systems, to appear in Mathematics of Control, Signals and Systems (1991).
J. Galambos, The Asymptotic Theory of Extreme Order Statistics, John Wiley & Sons, New York, (1978).
S. Geman, Some averaging and stability results for random differential equations, SIAM J. Appl. Math., 36 (1979) 87–105.
L. Gerencsér, Parameter Tracking of Time-Varying Continuous-Time Linear Stochastic Systems, In Modelling, Identification and Robust Control (eds. Ch. I. Byrnes and A. Lindquist), North Holland, (1986), 581–595.
L. Gerencsér, On a class of mixing processes. Stochastics, 26 (1989a), pp.165–191.
L. Gerencsér, Strong approximation of the recursive prediction error estimator of the parameters of an ARMA process. McGill Research Centre for Intelligent Machines, TR-CIM 89-8 Submitted for publication.
L. Gerencsér, On Rissanen's predictive stochastic complexity for stationary ARMA processes. McGill Research Centre for Intelligent Machines, TR-CIM-89-5. Submitted for publication.
L. Genercsér, On the martingale approximation of the estimation error of ARMA parameters. Systems and Control Letters, 15, (1990), 417–423.
L. Gerencsér, Rate of convergence of recursive estimators. Submitted for publication.
L. Gerencsér, Closed loop parameter identifiability and adaptive control of a linear stochastic system. Systems and Control Letters, 15, (1990), 411–416.
L. Gerencsér, Strong approximation of vector-valued stochastic integrals. To appear in Statistics and Probability Letters (1991).
L. Gerencsér, Strong approximation theorems for estimator processes in continuous time, Proc. of Limit Theorem in Probability and Statistics (eds. I. Berkes, E. Csáki and I. Révész), North Holland, (1991), to appear.
L. Gerencsér, Almost sure exponential stability of random linear differential equations. To appear in Stochastics, (1991)
L. Gerencsér, Fixed gain estimation of ARMA parameters. Submitted for publication.
L. Gerencsér, Predictive stochastic complexity associated with fixed gain estimators. Submitted for publication.
L. Gerencsér, Predictive stochastic complexity for continuous-time systems. Submitted for publication (1991).
L. Gerencsér, and J. Baikovicius, Change and point detection with stochastic complexity. To appear in Proc. of 9-th IFAC/IFORS Symposium on Identification and System Parameter Estimation, Budapest, (1991), Pergamon Press, Oxford.
L. Gerencsér, and J. Baikovicius, Model selection, stochastic complexity, and badness amplification, Submitted to the 30th IEEE Conference on Decision and Control, (1991).
L. Gerencsér, I. Gyöngy, and Gy. Michaletzky, Continuous time Recursive Maximum Likelihood Method. A New Approach to Ljung's Scheme, Proc. of the 9th. IFAC World Congress, Budapest, 2, (eds. L. Ljung and K.J. Åström), Pergamon Press, Oxford, (1984), pp. 75–77.
L. Gerencsér and A. Heunis, Rate of convergence for the LMS algorithm, Manuscript (1991).
L. Gerencsér and J. Rissanen, A prediction bound for Gaussian ARMA processes. Proc. of the 25-th CDC, Athens, Vol. 3 (1986), pp.1487–1490.
L. Gerencsér and J. Rissanen, Asymptotics of predictive stochastic complexity. To appear in “New Directions in Time Series Analysis”, Proc. of the 1990 IMA Workshop (eds. E. Parzen, D. Brillinger, M. Rosenblatt, M. Taqqu, J. Geweke and P.E. Caines,). Springer, (1991).
L. Gerencsér and Zs. Vágó A strong approximation theorem for estimators in continuous time, Submitted for publication.
L. Gerencsér, and Zs. Vágó, From fine asymptotics to model selection. To appear in “Identification of Continuous-Time Systems” (ed. N.K. Sinha), Kluwer Academic Publishers, Dordrecht, The Netherlands, (1991).
L. Gertler and Cs. Bányász, A recursive maximum likelihood estimator, Automatica, (1971).
G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall Englewood Cliffs, NJ (1984).
E.J. Hannan, The convergence of some time-series recursions, Ann. Stat., 4, (1976) 1258–1270.
E.J. Hannan, and M. Deistler, The statistical theory of linear systems. Wiley (1988).
E.J. Hannan, A.J. McDougall and D.S. Poskitt, Recursive estimation of autoregressions. J. Roy, Stat. Soc. Ser B. 51 (1990).
E.M. Hemerley and M.A.H. Davis, Strong consistency of the PLS criterion for order determination of autoregressive processes, Ann. Stat., 17, (1989) 941–946.
A. Heunis, Rates of convergence for an adaptive filtering algorithm driven by stationary finite-memory data. Submitted for publication.
A. Heunis, Asymptotic Properties of Prediction Error Estimators in Approximate System Identification. Stochastics,24 (1988),pp.1–43.
I. Hunter, S. Lafontaine and J. Hollerbach, Microrobotics and the study of muscle: special problems in control, system identification and modelling, To appear in: Proc. of the 9th IFAC/IFORS Symposium on Identification and System Parameter Estimation, Budapest, (1991)., Pergamon Press, Oxford.
I.A. Ibragimov and R.Z. Khasminskii, Statistical Estimation. Asymptotic Theory, Springer Verlag, Berlin (1981).
H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, MIT Press, (1984).
H.J. Kushner and D.S. Clark, Stochastic approximation methods for constrained and unconstrained optimization, Springer, (1978).
L. Kavalieris, The estimation of the order of an autoregression using recursive residuals and cross-validation. J. of Time Series analysis, 10 (1989), pp.271–281.
Yu. A. Kutoyants, Estimation of stochastic processes. Publishing House of the Armenian Academy of Sciences, Yerevan (in Russian, 1980) and Heldermann, Berlin (1989).
T.Z. Lai and C.Z. Wei, Least squares estimates in stochastic regression models with application to identification and control of dynamic systems, Ann. of Stat., 10 (1982) 154–165.
L. Ljung On Consistency and Identifiability, Mathematical Programming Study, 5, (1976) 169–190.
L. Ljung, Analysis of recursive stochastic algorithms, IEEE Trans. Aut. Cont., AC-22 (1977), pp.551–575.
L. Ljung and P. Caines, Asymptotic normality of prediction error estimation for approximate system models, Stochastics, 31 (1979), pp.29–46.
D.L. McLeish, A maximal inequality and dependent strong laws, The Annals of Probability, 3 (1975), pp.829–839.
J.B. Moore, On strong consistency of least squares identification algorithms, Automatica, 14 (1978), pp.505–509.
F. Móricz, Moment Inequalities and the strong laws of large numbers, Z. Wahrsche-inlichkeitstheorie u. verw. Gebiete, 35 (1974), pp.299–314.
J. Rissanen, Modelling by shortest data description, Automatica, 14 (1978), pp.465–471.
J. Rissanen, Order estimation by accumulated prediction errors, Essays in Time Series and Allied Processes (eds. J. Gani, M.B. Priestley), pp.55–61 (1984).
J. Rissanen, Stochastic complexity and modeling, Annals of Statistics 14 (1986), pp.1080–1100.
J. Rissanen, Stochastic complexity in statistical inquiry. World Scientific Publisher (1989).
J. Rissanen, and P.E. Caines, The strong consistency of maximum likelihood estimators for ARMA processes. Ann Statist. 7 (1979) 297–315.
T. Söderström, An On-line Algorithm for Approximate Maximum-Likelihood Identification of Linear Dynamic Systems Report 7308, (1973) Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.
T. Söderström and P. Stoica, System identification (1989), Prentice Hall.
V. Solo, The second order properties of a time series recursion, Ann. Stat. 9 (1981) 307–317.
Zs. Vágó and L. Gerencsér, Uniqueness of the Maximum-Likelihood Estimates of the Kalman-gain Matrix of a State Space Model, Proc. of the IFAC/IFORS, Conference of Dynamic Modelling of National Economics, Budapest, (1985).
D.G. DeWolf and D.M.Wiberg An ordinary differential equation technique for continuous time parameter estimation, IEEE Trans. Aut. Cont., submitted.
G. Yin, and Y.M. Zhu, On robustness of the Robbins-Monro method for parallel processing, Systems and Control Letters, 12 (1989), pp. 77–86.
K. Yoshihara, Moment inequalities for mixing sequences, Kodai Math. J. 1 (1978) 316–328.
G. Zames, and L.Y. Wang, Local-Global Double Algebras for Slow H ∞ Adaptation: Part I-Inversion and Stability, IEEE Trans. Aut. Cont., 36, 2, (1991), pp. 130–142.
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Gerencsér, L. (1991). Strong approximation results in estimation and adaptive control. In: Gerencséer, L., Caines, P.E. (eds) Topics in Stochastic Systems: Modelling, Estimation and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009308
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