摘要： It is well known that a regular diffusion on an interval I without killing inside is uniquely determined by a canonical scale function s and a canonical speed measure m. Note that s is a strictly increasing and continuous function and m is a fully supported Radon measure on I. In this talk, we will associate a general triple (I, s, m), where s is only assumed to be strictly increasing and m is not necessarily fully supported, to certain Markov processes by way of resolvent approach. This talk is based on a joint work with Li Liping.