Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Laplace’s method for iterated complex Brownian integrals
Download PDF
Download PDF
  • Published: 03 May 2005

Laplace’s method for iterated complex Brownian integrals

  • Grégory Liorit1 

Probability Theory and Related Fields volume 133, pages 18–42 (2005)Cite this article

  • 96 Accesses

  • Metrics details

Abstract.

A kind of Laplace’s method is developped for iterated stochastic integrals where integrators are complex standard Brownian motions. Then it is used to extend properties of Bougerol and Jeulin’s path transform in the random case when simple representations of complex semisimple Lie algebras are not supposed to be minuscule.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Anker, J.-Ph., Bougerol, Ph., Jeulin, T.: The infinite Brownian loop on a symmetric space. Rev. Mat. Iberoamericana 18 (1), 41–97 (2002)

    Google Scholar 

  2. Arnaudon, M.: Semi-martingales dans les espaces homogènes. Ann. Inst. Henri Poincarré 29 (2), 269–288 (1993)

    Google Scholar 

  3. Baryshnikov, Y.: GUEs and queues. Probab. Theory Relat. Fields 119, 256–274 (2001)

    Google Scholar 

  4. Biane, Ph.: Quelques propriétés du mouvement brownien dans un cône. Stochastic Process. Appl. 53, 233–240 (1994)

    Article  Google Scholar 

  5. Biane, Ph., Bougerol, P., O’connell, N.: Littelmann paths and Brownian paths. Preprint

  6. Bougerol, P., Jeulin, T.: Paths in Weyl chambers and random matrices. Probab. Theory Relat. Fields 124 (4), 517–543 (2002)

    Article  Google Scholar 

  7. Gravner, J., Tracy, C.A., Widom, H.: Limit theorems for height fluctuations in a class of discrete space and time growth models. J. Statist. Phys. 102, 1085–1132 (2001)

    Article  Google Scholar 

  8. Hakim-Dowek, M., et, Lepingle, D.: L’exponentielle stochastique des groupes de Lie. séminaire de probabilités 20, Lecture Notes in Math. 1204, 352–374 (1986)

  9. Littelmann, P.: Paths and root operators in representation theory. Ann. Math. 142, 499–525 (1995)

    Google Scholar 

  10. O’connell, N., Yor, M.: A representation for non–colliding random walks. Elect. Commun. Prob. 7, 1–12 (2002)

    Google Scholar 

  11. Onishchik, A.L., Vinberg, E.B.: Lie groups and algebraic groups. Springer-Verlag, Berlin, 1990

  12. Pitman, J.W.: One–dimensional Brownian motion and the three-dimensional Bessel process. Advances in Appl. Probability 7, 511–526 (1975)

    Google Scholar 

  13. Revuz, D., Yor, M.: Continuous martingales and Brownian motion. Third Edition, Grundlehren des Mathematischen Wissenschaften 293, Springer-Verlag, Berlin, 1999

  14. Varadarajan, V.S.: Lie groups, Lie algebras and their representations. Graduate Text in Mathematics, 102, Springer-Verlag, New-York, 1984

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université de Poitiers, SP2MI, Boulevard Pierre et Marie Curie, Téléport 2 - BP 30 179, 86962, Futuroscope cedex, France

    Grégory Liorit

Authors
  1. Grégory Liorit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Grégory Liorit.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Liorit, G. Laplace’s method for iterated complex Brownian integrals. Probab. Theory Relat. Fields 133, 18–42 (2005). https://doi.org/10.1007/s00440-004-0409-0

Download citation

  • Received: 03 September 2004

  • Revised: 04 November 2004

  • Published: 03 May 2005

  • Issue Date: September 2005

  • DOI: https://doi.org/10.1007/s00440-004-0409-0

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Mathematics Subject Classification (2000):

  • (primary) 60H05
  • 15A52
  • 17B10
  • 60B99
  • 60J65
  • (secondary) 22E30
  • 22E46
  • 43A85

Key words or phrases

  • Random matrix
  • Gaussian Unitary Ensemble
  • Symmetric space
  • Weyl chamber
  • Complex semisimple group
  • Representation theory
  • Pitman’s theorem
  • Iterated stochastic integrals
  • Laplace’s method
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature