On skorohod embedding in n-dimensional brownian motion by means of natural stopping times

  • Neil Falkner
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 784)


Let μ be a measure on ℝn whose electrostatic potential is well-defined and not everywhere infinite. Let (Bt) be Brownian motion in ℝn with law(B0)=μ. We give sufficient conditions for a measure v on ℝn to be of the form law(BT) where T is a natural (ie., non-randomized) stopping time for (Bt) which is not "too big". (If n≥3, any stopping is not "too big" but if n=1 or 2, some stopping times are "too big"). If the measure μ does not charge polar sets, the conditions we give are not only sufficient but necessary.


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Copyright information

© Springer-Verlag 1980

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  • Neil Falkner

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