LEADER 04142nam 22006135 450 001 9911047689003321 005 20251118120409.0 010 $a9783032000521 024 7 $a10.1007/978-3-032-00052-1 035 $a(CKB)43368487200041 035 $a(MiAaPQ)EBC32420107 035 $a(Au-PeEL)EBL32420107 035 $a(DE-He213)978-3-032-00052-1 035 $a(EXLCZ)9943368487200041 100 $a20251118d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHidden Markov Processes and Adaptive Filtering /$fby Yury A. Kutoyants 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (1042 pages) 225 1 $aSpringer Series in Statistics,$x2197-568X 311 08$a9783032000514 327 $a1 Auxiliary Result -- 2 Small Noise in Both Equations -- 3 Small Noise in Observations -- 4 Hidden Ergodic O-U process -- 5 Hidden Telegraph Process -- 6 Hidden AR Process -- 7 Source Localization. 330 $aThis book is devoted to the problem of adaptive filtering for partially observed systems depending on unknown parameters. Adaptive filters are proposed for a wide variety of models: Gaussian and conditionally Gaussian linear models of diffusion processes; some nonlinear models; telegraph signals in white Gaussian noise (all in continuous time); and autoregressive processes observed in white noise (discrete time). The properties of the estimators and adaptive filters are described in the asymptotics of small noise or large samples. The parameter estimators and adaptive filters have a recursive structure which makes their numerical realization relatively simple. The question of the asymptotic efficiency of the adaptive filters is also discussed. Readers will learn how to construct Le Cam?s One-step MLE for all these models and how this estimator can be transformed into an asymptotically efficient estimator process which has a recursive structure. The last chapter covers several applications of the developed method to such problems as localization of fixed and moving sources on the plane by observations registered by K detectors, estimation of a signal in noise, identification of a security price process, change point problems for partially observed systems, and approximation of the solution of BSDEs. Adaptive filters are presented for the simplest one-dimensional observations and state equations, known initial values, non-correlated noises, etc. However, the proposed constructions can be extended to a wider class of models, and the One-step MLE-processes can be used in many other problems where the recursive evolution of estimators is an important property. The book will be useful for students of filtering theory, both undergraduates (discrete time models) and postgraduates (continuous time models). The method described, preliminary estimator + One-step MLE-process + adaptive filter, will also be of interest to engineers and researchers working with partially observed models. 410 0$aSpringer Series in Statistics,$x2197-568X 606 $aMarkov processes 606 $aStochastic models 606 $aStatistics 606 $aProbabilities 606 $aMarkov Process 606 $aStochastic Modelling in Statistics 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 606 $aProbability Theory 615 0$aMarkov processes. 615 0$aStochastic models. 615 0$aStatistics. 615 0$aProbabilities. 615 14$aMarkov Process. 615 24$aStochastic Modelling in Statistics. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aProbability Theory. 676 $a519.233 700 $aKutoyants$b Yu. A$0442032 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911047689003321 996 $aHidden Markov Processes and Adaptive Filtering$94469174 997 $aUNINA