2018/06/25 by Vladislav B. Tadić, Vladislav Z. B. Tadic, Arnaud Doucet +2
Computer Science · Engineering · Mathematics · #Algorithm #Analytic continuation #Applied mathematics #Artificial intelligence #Computer science #Continuation #Control Systems and Identification #Cover (algebra) #Engineering #Entropy (arrow of time) #FOS: Computer and information sciences #FOS: Mathematics #Hidden Markov model #Hidden semi-Markov model #Inference #Information Theory (cs.IT) #Information theory #Markov Chains and Monte Carlo Methods #Markov chain #Markov model #Markov process #Mathematical analysis #Mathematics #Maximum-entropy Markov model #Parameterized complexity #Physics #Statistical physics #Statistics #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks #Variable-order Markov model #cs.IT #math.IT #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1806.09589
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2018/06/25 · arxiv created 2019/08/29 · arxiv updated 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory.