  We introduce a new family of integrable stochastic processes, called
\textit{dynamical stochastic higher spin vertex models}, arising from fused
representations of Felder's elliptic quantum group $E_{\tau, \eta}
(\mathfrak{sl}_2)$. These models simultaneously generalize the stochastic
higher spin vertex models, studied by Corwin-Petrov and Borodin-Petrov, and are
dynamical in the sense of Borodin's recent stochastic interaction round-a-face
models.
  We provide explicit contour integral identities for observables of these
models (when run under specific types of initial data) that characterize the
distributions of their currents. Through asymptotic analysis of these
identities in a special case, we evaluate the scaling limit for the current of
a dynamical version of a discrete-time partial exclusion process. In
particular, we show that its scaling exponent is $1 / 4$ and that its one-point
marginal converges (in a sense of moments) to that of a non-trivial random
variable, which we determine explicitly.
