Cox, A. M. G., Hobson, D. and Obłój, J., 2011. Time-homogeneous diffusions with a given marginal at a random time. ESAIM: Probability and Statistics, 15, S11-S24.
We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (X_t) which, stopped at an independent exponential time T, is distributed according to μ. The process (X_t) is specified via its speed measure m. 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, Ann. Probab. 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof exploiting applications of Krein's spectral theory of strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument.
|Item Type ||Articles|
|Creators||Cox, A. M. G., Hobson, D. and Obłój, J.|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||ps0951.pdf: Copyright is owned by `ESAIM: Probability and Statistics'. The original publication is available at: www.edpsciences.org/ps|
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