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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, 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof exploiting...
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