On exponential families of Markov processes

✍ Scribed by Uwe Küchler; Michael Sørensen

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 782 KB
• Volume: 66
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00072-4

✦ Synopsis

Exponential families of stochastic processes in discrete and continuous time are considered, where the underlying observed process is Markovian under the dominating measure. It is shown that the observed process is Markovian under the other probability measures in the exponential family if and only if the canonical process is an additive functional. If the observed process is not Markovian under all measures in the family, certain components of the canonical process will not be an additive functional. Also the structure of the likelihood function for exponential families of Markov processes in terms of L6vy systems is considered. Several examples are included. ~7) 1998 Elsevier Science B.V.