Unbiased shifts of Brownian motion

  title={Unbiased shifts of Brownian motion},
  author={G{\"u}nter Last and Peter M{\"o}rters and Hermann Thorisson},
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


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 29 references

Representation of measures by balayage from a regular recurrent point

J. Bertoin, Y. Le Jan
Ann. Probab. 20, • 1992
View 6 Excerpts
Highly Influenced

Two uniform intrinsic constructions for the local time of a class of Lévy processes

M. T. Barlow, E. A. Perkins, S. J. Taylor
Illinois J. of Math • 1986
View 10 Excerpts
Highly Influenced

A Tauberian Theorem and Its Probability Interpretation

View 2 Excerpts

Similar Papers

Loading similar papers…