Conformance is defined as a measure of distance between the behaviors of two
dynamical systems. The notion of conformance can accelerate system design when
models of varying fidelities are available on which analysis and control design
can be done more efficiently. Ultimately, conformance can capture distance
between design models and their real implementations and thus aid in robust
system design. In this paper, we are interested in the conformance of
stochastic dynamical systems. We argue that probabilistic reasoning over the
distribution of distances between model trajectories is a good measure for
stochastic conformance. Additionally, we propose the non-conformance risk to
reason about the risk of stochastic systems not being conformant. We show that
both notions have the desirable transference property, meaning that conformant
systems satisfy similar system specifications, i.e., if the first model
satisfies a desirable specification, the second model will satisfy (nearly) the
same specification. Lastly, we propose how stochastic conformance and the
non-conformance risk can be estimated from data using statistical tools such as
conformal prediction. We present empirical evaluations of our method on an F-16
aircraft, an autonomous vehicle, a spacecraft, and Dubin's vehicle