Mathematical statistics and stochastic processes (Q2857989)

This is a book about statistics and stochastic processes. It studies inference of variables observed along the time, such that, they are correlated. Definitely, it is not a book for beginners. Mathematical statistics, inference for stochastic processes and elements of probability theory are presented in a rigorous and concise style. The measure theoretic approach is used both in the formulation of mathematical statistics and stochastic processes. It starts with decision theory and continues with classical theory of estimations and tests; asymptotics, both parametric and nonparametric, and then goes through statistics for discrete-time stationary processes and Poisson processes. Then follows with statistics for continuous-time processes, namely, Itō's integrals, second order and diffusion processes. The last chapters are dedicated to statistical prediction and to elements of probability theory. Maybe a bit more results on inference related to stationary and second order processes could be provided. Unfortunately, typos show up along the text. Hopefully, they are going to be corrected in the future editions of the book.