Process mining leverages event logs extracted from information systems to generate insights into the business processes of organizations. These insights are enhanced by explicitly accounting for the frequency of behavior captured in stochastic process models constructed from event logs. Causal nets are an elegant declarative process modeling formalism that relies on a small number of modeling constructs, yet is expressive. In this paper, we extend this formalism to the stochastic setting, that is, to allow the extended nets to capture the likelihoods of the observed process. We also propose a stochastic causal net discovery approach using Markovian abstraction. Our approach begins with a standard causal net model generated by a control flow discovery algorithm, and then employs optimization techniques to determine optimal binding weights. These weights enable the stochastic interpretation of the model to closely approximate the Markovian abstraction of the original event log. Our technique has been implemented and made publicly available. The evaluation based on this implementation demonstrates the feasibility of the technique. Compared to baseline models, the discovered models achieve noticeable improvements in the quality of stochastic conformance.