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1 results

  • On a formula of Takács for Brownian motion with drift

  • Part of
  • R. A. Doney, M. Yor
  • Journal:
    Journal of Applied Probability / Volume 35 / Issue 2 / June 1998
    Published online by Cambridge University Press:
    14 July 2016, pp. 272-280
    Print publication:
    June 1998

  • A recent result of Takács (1995) gives explicitly the density of the time spent before t above a level x ≠ 0 by Brownian motion with drift. Takács' proof is by means of random walk approximations to Brownian motion, but in this paper we give two different proofs of this result by considerations involving only Brownian motion. We also give a reformulation of Takács' result which involves Brownian meanders, and an extension of Denisov's representation of Brownian motion in terms of two independent Brownian meanders.