  We construct planar semimartingales that include the Walsh Brownian motion as
a special case, and derive Harrison-Shepp-type equations and a
change-of-variable formula in the spirit of Freidlin-Sheu for these so-called
"Walsh semimartingales". We examine the solvability of the resulting system of
stochastic integral equations. In appropriate Markovian settings we study two
types of connections to martingale problems, questions of uniqueness in
distribution for such processes, and a few examples.
