Time-homogeneous diffusions with a given marginal at a random time
We solve explicitly the following problem: for a given probability measure , we specify a generalised martingale diffusion () which, stopped at an independent exponential time , is distributed according to . The process ( ) is specified its speed measure . We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we...