• Bernoulli
  • Volume 6, Number 4 (2000), 615-620.

An extension of P. Lévy's distributional

Svend Erik Graversen and Albert N. Shiryaev

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We extend the well-known P. Lévy theorem on the distributional identity ( M t-B t,M t)simeq(|B t|,L(B) t) , where ( B t) is a standard Brownian motion and ( M t)=(sup 0 stB s) to the case of Brownian motion with drift λ. Processes of the type

d X t λ=-λsgn(X t λ)dt+dB t

appear naturally in the generalization.

Article information

Bernoulli, Volume 6, Number 4 (2000), 615-620.

First available in Project Euclid: 8 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Brownian motion local time Markov processes


Erik Graversen, Svend; Shiryaev, Albert N. An extension of P. Lévy's distributional. Bernoulli 6 (2000), no. 4, 615--620.

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