One-Dimensional Continuous Strong Markov Processes

One-dimensional temporally homogeneous strong Markov processes with continuous path functions are considered. No regularity conditions are assumed. Infinitesimal operators for all these processes are calculated. These calculations are based on a preliminary analysis of the local behaviour of path functions. The general results of sections 1–3 are used in sections 4–5 for conducting a more detailed investigation of the process in intervals of its regularity.