Can time-homogeneous diffusions produce any distribution?
Given a centered distribution, can one find a time-homogeneous
martingale diffusion starting at zero, which has the given law at time 1?
We answer the question affirmatively if generalised diffusions are allowed.
The original motivation for us to study this problem comes from a
problem in mathematical finance.
Joint work with Erik Ekström, David Hobson and Svante Janson.