Conformance checking focuses on quantifying behavioral differences between desired and observed process behavior. Stochastic conformance checking considers not only the desired control flow of a process but also the relative frequency of each sequence. State-of-the-art stochastic conformance measures either cannot gracefully handle partially matching traces or are prohibitively expensive to compute. This paper bridges this gap by introducing the stochastic Markovian abstraction. The abstraction is defined as the relative occurrences of sub-traces in a stochastic language. Two stochastic languages can be compared via their Markovian abstractions using existing language comparison techniques. We show how to compute this abstraction for bounded, livelock-free stochastic labeled Petri nets. One of its derived measures is qualitatively and quantitatively evaluated on a series of artificial and real-world datasets. The experiments show that the abstraction can be efficiently computed and is successful in handling partially mismatching traces.