Continuous One-Dimensional Markov Processes and Additive Functionals Derived from Them

The terminology and symbols employed are the same as in [1] and [2].
The paper describes all continuous Feller one-dimensional Markov processes, which are regular within a segment and gives their infinitesimal operators (Theorem 4). It is stated that each such process is a sub-process of a non-terminating process of the same type (Theorems and 1'). Therefore, a description of all processes amounts to a description of all multiplicative or additive functionals corresponding to regular Feller sub-processes of non-terminating processes.