Exponential Families of Stochastic Processes

• Main Authors: Küchler, Uwe (Author), Sørensen, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 1997.
• Series: Springer Series in Statistics,
• Subjects: Mathematics.; Applied mathematics.; Engineering mathematics.; Probabilities.; Probability Theory and Stochastic Processes.; Applications of Mathematics.

Exponential families of stochastic processes are parametric stochastic p- cess models for which the likelihood function exists at all ?nite times and has an exponential representation where the dimension of the canonical statistic is ?nite and independent of time. This de?nition not only covers many...

Table of Contents:

• 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.