Exponential Families of Stochastic Processes

A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.

Inhalt

Natural Exponential Families of Léevy Processes.- Definitions and Examples.- First Properties.- Random Time Transformations.- Exponential Families of Markov Processes.- The Envelope Families.- Likelihood Theory.- Linear Stochastic Differential Equations with Time Delay.- Sequential Methods.- The Semimartingale Approach.- Alternative Definitions.