  Typically, a stochastic model relates stochastic "inputs" and, perhaps,
controls to stochastic "outputs". A general version of the Yamada-Watanabe and
Engelbert theorems relating existence and uniqueness of weak and strong
solutions of stochastic equations is given in this context. A notion of {\em
compatibility} between inputs and outputs is critical in relating the general
result to its classical forebears. The relationship between the compatibility
condition and the usual formulation of stochastic differential equations driven
by semimartingales is discussed.
