Bernoulli

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

An extension of P. Lévy's distributional

Svend Erik Graversen and Albert N. Shiryaev

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 8 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081449596

Mathematical Reviews number (MathSciNet)
MR2002h:60171

Zentralblatt MATH identifier
0965.60077

Keywords
Brownian motion local time Markov processes

Citation

Erik Graversen, Svend; Shiryaev, Albert N. An extension of P. Lévy's distributional. Bernoulli 6 (2000), no. 4, 615--620. https://projecteuclid.org/euclid.bj/1081449596


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References

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