MODERATE MARKOV PROPERTY AND RIGHT CONTINUITY OF NATURAL FILTRATIONS OF TWO-PARAMETER FELLER PROCESSES

In this paper it is shown that two-parameter Feller processes satisfying some additional conditions possess the moderate Markov property and a property which is similar to quasi-left continuity. It is shown that the wide-past natural filtrations of a kind of two-parameter Markov processes are right continuous. The kind includes Feller processes with right continuous sample functions.