Process mining is concerned with deriving formal models capable of reproducing the behaviour of a given organisational process by analysing observed executions collected in an event log. The elements of an event log are finite sequences (i.e., traces or words) of actions. Many effective algorithms have been introduced which issue a control flow model (commonly in Petri net form) aimed at reproducing, as precisely as possible, the language of the considered event log. However, given that identical executions can be observed several times, traces of an event log are associated with a frequency and, hence, an event log inherently yields also a stochastic language. By exploiting the trace frequencies contained in the event log, the stochastic extension of process mining, therefore, consists in deriving stochastic (Petri nets) models capable of reproducing the likelihood of the observed executions. In this paper, we introduce a novel stochastic process mining approach. Starting from a “standard” Petri net model mined through classical mining algorithms, we employ optimization to identify optimal weights for the transitions of the mined net so that the stochastic language issued by the stochastic interpretation of the mined net closely resembles that of the event log. The optimization is either based on the maximum likelihood principle or on the earth moving distance. Experiments on some popular real system logs show an improved accuracy w.r.t. to alternative approaches.