Doubly-Feller Process with Multiplicative Functional

Abstract

Despite the common use of the term “Feller property”, there are variations in its definition. In the early literature on Markov processes, there are discussions of this and related properties, often under sets of bewildering assumptions. The coast should now be clear, but certain neat formulations may have been overlooked. In §1 of this note, some old results are reviewed in more general forms and an apparently new one is derived. In §2, the results are extended to include a multiplicative functional, of which the prime example is that of Feynman-Kac, properly generalized.

This work was supported in part by NSF grant DMS83-01072 at Stanford University.