Research and Exposition in Mathematics -- Volume 6
Yu. A. Kutoyants
Parameter Estimation for Stochastic Processes
214 p., soft cover, ISBN 3-88538-206-7, 1984, out of print
The book begins with some elementary concepts from the theory of probability and mathematical
statistics and in particular some notions of asymptotic theory of statistical inference. The
later chapters deal with asymptotic properties of estimators for various types of continuous
time processes. The approach to asymptotic theory used throughout the book is via the
log-likelihood ratio process. Many examples illustrate the results.
The approach to the study of asymptotic theory of maximum likelihood and related estimators
via stochastic processes as adopted here is also of potiential use in other areas, for
instance, nonlinear regression.
The probabilist or the statistician interested in theoretical aspects will appreciate the
fact that this book gives a comprehensive treatment of asymptotic theory of statistical
inference for several types of continuous time processes. It will be of great interest to
mathematicians doing reseach in this area but can also be used for one semester courses for
"... gives a comprehensive treatment of asymptotical theory of statistical inference
for diffusion and Poisson type processes. It will be of great interest to mathematicians
doing research in this area, but can also be used for courses for graduate students".
(Statistics & Decisions)
"... excellent book ...". (Statistics)