Unbiased shifts of Brownian motion

@inproceedings{Last2012UnbiasedSO,
  title={Unbiased shifts of Brownian motion},
  author={G{\"u}nter Last and Peter M{\"o}rters and Hermann Thorisson},
  year={2012}
}
Let B = (Bt)t∈R be a two-sided standard Brownian motion. An unbiased shift of B is a random time T , which is a measurable function of B, such that (BT+t−BT )t∈R is a Brownian motion independent of BT . We characterise unbiased shifts in terms of allocation rules balancing mixtures of local times of B. For any probability distribution ν on R we construct a stopping time T ≥ 0 with the above properties such that BT has distribution ν. We also study moment and minimality properties of unbiased… CONTINUE READING

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