Exponential families of stochastic processes
Exponential models play a central role in classical statistical theory. There are at least three reasons for studying the classical exponential families of probability distributions. They are analytically tractable models, they have several nice statistical properties, and a large part of the models used in statistical practice are exponential families. The authors study what role exponential families play in statistical inference for stochastic processes. The book contains 12 chapters and an appendix. A considerable portion of this one is focused on likelihood theory for general exponential families of stochastic processes. The other main themes are asymptotic likelihood theory and sequential maximum likelihood estimation. This book will assist graduate students as well as researchers in statistics not only in getting into the problems of inference for stochastic processes by studying the most tractable type of models, but also in learning to solve the problems by the tools of stochastic calculus. Most of the concepts from stochastic calculus are introduced and explained without proof in an appendix.
statistical inference for stochastic processes
likelihood theory for general exponential families
scientific article; zbMATH DE number 1049649