  Arcade processes are a class of continuous stochastic processes that
interpolate in a strong sense, i.e., omega by omega, between zeros at fixed
pre-specified times. Their additive randomization allows one to match any
finite sequence of target random variables, indexed by the given fixed dates,
on the whole probability space. The randomized arcade processes (RAPs) can thus
be interpreted as a generalization of anticipative stochastic bridges. The
filtrations generated by these processes are utilized to construct a class of
martingales which interpolate between the given target random variables. These
so-called filtered arcade martingales (FAMs) are almost-sure solutions to the
martingale interpolation problem and reveal an underlying stochastic filtering
structure. In the special case of conditionally-Markov randomized arcade
processes, the dynamics of FAMs are informed by Bayesian updating. The same
ideas are applied to filtered arcade reverse-martingales, which are constructed
in a similar fashion, using reverse-filtrations of RAPs, instead. As a
potential application of this theory, optimal transportation is explored: FAMs
may be used to introduce noise in martingale optimal transport, in a similar
fashion to how Schr\"odinger's problem introduces noise in optimal transport.
This information-based approach to transport is concerned with selecting an
optimal martingale coupling for the target random variables under the influence
of the noise that is generated by an arcade process, and suggests application
in finance or climate science, for instance.
