A Classification of Deterministic Hunt Processes with Some Applications

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 It\^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980) is proven.