Suppose we are given a multi-dimensional Ito process, which can be regarded as a model for an underlying asset price together with related stochastic processes, e.g., volatility. The drift and diffusion terms for this Ito process are permitted to be arbitrary adapted processes. We construct a weak solution to a diffusion-type equation that matches the distribution of the Ito process at each fixed time. Moreover, we show how to also match the distribution at each fixed time of statistics of the Ito process, including the running maximum and running average of one of the components of the process. A consequence of this result is that a wide variety of exotic derivative securities have the same prices when written on the original Ito process as when written on the mimicking process. This is joint work with Gerard Brunick.