Randal Douc, Eric Moulines, David Stoffer

"This book is very suitable for mathematicians requiring a very rigorous and complete introduction to nonlinear time series and their applications in several fields."—Zentralblatt MATH 1306"This book focuses on theory and methods, with applications in mind. It is quite theory-heavy, with many rigorously established theoretical results.… It is also very timely and covers many recent developments in nonlinear time series analysis… readers can get a very up-to-date view of the current developments in nonlinear time series analysis from this book."—Journal of the American Statistical Association, December 2014"… the book will definitely help readers who are very mathematically inclined and keen on rigour and interested in further pursuing the probabilistic aspects of nonlinear time series. I have no doubt the book will be useful and timely, and I have no hesitation in recommending the book … ."—T. Subba Rao, Journal of Time Series Analysis, 2014

• Preliminaries. Markov and Iterative Models: Nonlinear Markovian Models. Stability, Recurrence, Mixing. Ergodicity, Limit Theorems. Parametric Inference. Nonparametric Inference. Hidden Markov Models: Some HMM Models. Filtering and Smoothing in HMM. Parametric Inference for HMM. Nonparametric Inference for HMM. Particle Filtering Basics. Advanced Issues in Particle Filtering. Particle Smoothing Basics. Numerical Methods for Inference.