2009/12/09 by Alexander M. G. Cox, Cox, Alexander M. G., David Hobson +5
Mathematics · Physics and Astronomy · #60G40 (Primary) 60G44 #60J60 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Opinion Dynamics and Social Influence #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60G40 #msc:60G44 #msc:60J60
paper · pdf · doi:10.48550/arxiv.0912.1719
15 pages, 2 figures
arxiv created 2009/12/09 · openalex publication_date 2009/12/09 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T, is distributed according to mu. The process X is specified via its speed measure m. We present three proofs. First we show how the result can be derived from the solution of Bertoin and Le Jan (1992) 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.