Identification of dynamical systems with small noise

This volume is devoted to the study of parametric and nonparametric estimation through the observation of diffusion-type processes. The properties of maximum likelihood, Bayes, and minimum distance estimators are considered in the context of the asymptotics of small noise. It is shown that, under certain conditions relating to regularity, these estimators are consistent and asymptotically normal. Their properties in nonregular cases are also discussed.

Here nonregularity means the absence of derivatives with respect to parameters, random initial value, incorrectly specified observations, nonidentifiable models, etc. The book has seven chapters. The first chapter presents some auxiliary results needed in the subsequent work. Chapter 2 is devoted to the asymptotic properties of estimators in standard and nonstandard situations. Chapter 3 considers expansions of the maximum likelihood estimator and the distribution function. Chapters 4 and 5 cover nonparametric estimation and the disorder problem. Chapter 6 discusses problems of parameter estimation for linear and nonlinear partially observed models.

The final chapter studies the properties of a wide range of minimium distance estimators. The volume concludes with a remarks section, references and index.

. This volume will be of interest to statisticians, researchers in probability theory and stochastic processes, systems theory and communication theory.