Limiting distributions associated with moments of exponential

Y. Hariya, M. Yor

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

During the last decade, a number of explicit results about the distributions of exponential functionals of Brownian motion with drift: A t(μ) = ∫0t ds exp {2(B s + μs)}, have been obtained, often originating with the works of D. Dufresne. In the present paper, we rely extensively on these results to show the existence of limiting measures as T → ∞, when the law of {B t + μt, 0 ≦ t ≦ T} is perturbed by the Radon-Nikodym density consisting of either of the normalized functionals exp (-αA T(μ)) or 1/(AT(μ)) m. The results exhibit different regimes according to whether μ ≧ 0, or μ < 0 in the first case, and to a partition of the (μ, m)-plane in the second case. Although a large number of similar studies have been made for, say, one-dimensional diffusions, the present study, which focuses upon Brownian exponential functionals, appears to be new.

Original languageEnglish
Pages (from-to)193-242
Number of pages50
JournalStudia Scientiarum Mathematicarum Hungarica
Volume41
Issue number2
DOIs
Publication statusPublished - 2004 Jul 9
Externally publishedYes

Keywords

  • Exponential Brownian functionals
  • Gibbsian-like measures
  • Renormalized Wiener measure
  • Weak limits

ASJC Scopus subject areas

  • Mathematics(all)

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