W. Feller's decomposition into a road map and speed measure are adapted to symmetric Markov chains with instantaneous states. The road map is a family of matrices defined by time changing the process with measures concentrated on finite sets.
"Symmetric Markov Chains." Ann. Probab. 2 (4) 681 - 701, August, 1974. https://doi.org/10.1214/aop/1176996612