A Classification of Deterministic Hunt Processes with Some Applications
2011, v.17, Issue 2, 259-276
Deterministic processes form an important building block of several classes of processes. We provide a method to classify deterministic Hunt processes. Within this framework we characterize different subclasses (e.g. Feller) and construct some (counter-)examples. In particular the existence of a Hunt semimartingale (on R) which is not an Ito process in the sense of Cinlar, Jacod, Protter and Sharpe [E. Cinlar, J. Jacod, P. Protter and M.J. Sharpe, Semimartingales and Markov processes. Z. Wahrsch. Verw. Geb., 1980, v.54, pp. 161-219] is proven.
Keywords: Hunt semimartingale,deterministic process,Ito process,Feller semigroup,semimartingale characteristics,symbol