Let (X,Y) be following a 2-dimensional normal inverse gaussian distribution. Is the distribution of $X \lvert Y$ known?
Given it is not, is it representable in some semi-convenient way, specificially I will ultimately need the characteristic function so anything regarding that would work. A reference would suffice and be appreciated.
Edit: A tractable way of numerically evaluating the characteristic function might even be enough - all of the above would of course be better though.