Statistical inference for ergodic diffusion processes.
This work is a continuation of the study of large sample theory of continuous time stochastic processes investigated by the author in his books, Parameter estimation for stochastic processes. Transl. from the Russian (1984; Zbl 0542.62073); Identification of dynamical systems with small noise. (1994; Zbl 0831.62058); and Statistical inference for spatial Poisson processes. (1998; Zbl 0904.62108). The problems of parametric and nonparametric inference for diffusion processes were discussed recently in the reviewer's monograph, Statistical inference for diffusion type processes (1999; Zbl 0952.62077). It deals with the large sample theory for homogeneous ergodic diffusion processes, more specifically, asymptotically efficient statistical inference for one-dimensional ergodic diffusion processes. A large part of the book is based on work done by the author himself and work done in collaboration with his other colleagues and students. The contents of the book are as follows: Chapter 1: Diffusion processes and statistical problems; Chapter 2: Parameter estimation; Chapter 3: Special models; Chapter 4: Nonparametric estimators; Chapter 5: Hypothesis testing. The book is written in a very clear style and is of use for research workers in the area of inference for stochastic processes. However, it is not a textbook for class room use as it does not encompass wider coverage of inference problems for other classes of processes as in other books dealing with inference for stochastic processes.
scientific article; zbMATH DE number 2023345