In order to obtain a stochastic model that accounts for the stochastic aspects of the dynamics of a business process, usually the following steps are taken. Given an event log, a process tree is obtained through a process discovery algorithm, i.e., a process tree that is aimed at reproducing, as accurately as possible, the language of the log. The process tree is then transformed into a Petri net that generates the same set of sequences as the process tree. In order to capture the frequency of the sequences in the event log, weights are assigned to the transitions of the Petri net, resulting in a stochastic Petri net with a stochastic language in which each sequence is associated with a probability. In this paper we show that this procedure has unfavorable properties. First, the weights assigned to the transitions of the Petri net have an unclear role in the resulting stochastic language. We will show that a weight can have multiple, ambiguous impact on the probability of the sequences generated by the Petri net. Second, a number of different Petri nets with different number of transitions can correspond to the same process tree. This means that the number of parameters (the number of weights) that determines the stochastic language is not well-defined. In order to avoid these ambiguities, in this paper, we propose to add stochasticity directly to process trees. The result is a new formalism, called stochastic process trees, in which the number of parameters and their role in the associated stochastic language is clear and well-defined.