  Concurrency and probability are both much studied extensions of sequential
computation. Within concurrency theory, there is a broad divide between
interleaving models and logics, which model concurrency by non-determinism, and
`truly concurrent' models, in which concurrency (and/or causality) are directly
represented. True concurrency gives much richer models and logics, but is also
harder to work with, as the interactions of causality and concurrency can
become complex.
  In probabilistic computation, we have by now many well understood
probabilistic models and logics on interleaving models, developed over the last
thirty years or so. However, for true concurrency, adding probability has been
much harder, owing to the interactions between probabilistic independence and
causal/concurrent independence, piling both conceptual and technical
difficulties upon an already complex model. Various notions of, e.g.,
probabilistic Petri net have been introduced, but for simpler cases such as
free-choice nets.
  A significant contribution in the last decade was Abbes and Benveniste 2006,
which gave a rigorous foundation for probabilistic concurrency in terms of
Winskel's event structures, which can be seen as the lowest level of
concurrent/causal modelling. However, event structures are themselves not ideal
for representing richer high-level models such as (arbitrary) Petri nets, as
the concurrency is derived from a binary conflict relation.
  Here we develop an extension of the theory of Abbes and Benveniste to a more
general class of models, a certain subclass of `stable event structures'. This
class is sufficient to give a semantics to probabilistic Petri nets (including
the notoriously awkward notion of confusion, which is forbidden by free-choice
nets), and thereby allows the definition of general probabilistic logics for
Petri nets.
