  Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited.
In particular, we are interested in density expansions of the projection
$(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are
found which replace the well-known "not-in-cutlocus" condition known from
heat-kernel asymptotics. Our small noise expansion allows for a "second order"
exponential factor. As application, new light is shed on the Takanobu--Watanabe
expansion of Brownian motion and Levy's stochastic area. Further applications
include tail and implied volatility asymptotics in some stochastic volatility
models, discussed in a compagnion paper.
