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Table of Contents
1 Main Definitions and Notations
1.1 Markov Chains
1.1.1 Transition Kernels
1.1.2 Homogeneous Markov Chains
2 State Inference
3 Forgetting of the initial condition and filter stability
4 Sequential Monte Carlo Methods
5 Parameter Inference
6 Maximum Likelihood Inference, Part I: Optimization Through Exact Smoothing
7 Statistical Properties of the Maximum Likelihood Estimator
8 Elements of Markov Chain Theory
Summary
This document covers various topics related to hidden Markov models, including Markov chains, state inference, filter stability, sequential Monte Carlo methods, parameter inference, maximum likelihood optimization, and statistical properties of estimators. It provides detailed definitions, notations, and mathematical concepts essential for understanding and applying these models in practice.