  In this note we introduce a new approach to rough and stochastic partial
differential equations (RPDEs and SPDEs): we consider general Banach spaces as
state spaces and -- for the sake of simiplicity -- finite dimensional sources
of noise, either rough or stochastic. By means of a time-dependent
transformation of state space and rough path theory we are able to construct
unique solutions of the respective R- and SPDEs. As a consequence of our
construction we can apply the pool of results of rough path theory, in
particular we obtain strong and weak numerical schemes of high order converging
to the solution process.
