Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-31T17:26:00.938Z Has data issue: false hasContentIssue false
  • English
  • Français

Renormalization Of The Local Time For The d-Dimensional Fractional Brownian Motion With N Parameters

Published online by Cambridge University Press:  11 January 2016

M. Eddahbi ,
R. Lacayo ,
J. L. Solé ,
J. Vives  and
C. A. Tudor
M. Eddahbi
Affiliation:
Département de Mathématiques et Informatique Faculté des Sciences et Techniques, Université Cadi Ayyad, B. P. 549 Marrakech Maroc
R. Lacayo
Affiliation:
Departament de Matemàtiques Universitat Autànoma de Barcelona 08193 Bellaterra, Barcelona Spain
J. L. Solé
Affiliation:
Departament de Matemàtiques Universitat Autànoma de Barcelona 08193 Bellaterra, Barcelona Spain
J. Vives
Affiliation:
Departament de Matemàtiques Universitat Autànoma de Barcelona 08193 Bellaterra, Barcelona Spain
C. A. Tudor
Affiliation:
Samos/Matisse. 90, rue de Tolbiac Université de Panthéon-Sorbonne. Paris 1 75634 Paris Cedex 13 France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the asymptotic behavior in Sobolev norm of the local time of the d-dimensional fractional Brownian motion with N-parameters when the space variable tends to zero, both for the fixed time case and when simultaneously time tends to infinity and space variable to zero.

Keywords

60H0560H10

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 186 , 2007 , pp. 173 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[1] Eddahbi, M., Lacayo, R., Solé, J. L., Tudor, C. A. and Vives, J., Regularity of the local time for the d-dimensional fractional Brownian motion with N-parameters, to appear in Stoc. Analysis and Appl., (2005).CrossRefGoogle Scholar
[2] Hu, Y. and Oksendal, B., Chaos expansion of local time of fractional brownian motion, Stochastic Analysis and Applications, 20 (2002), no. 6, 815–837.Google Scholar
[3] Imkeller, P. and Weisz, F., The asymptotic behaviour of local time and occupation integrals of the N-parameter Wiener process in Rd , Prob. Theo. Rela. Fields, 98 (1994), 47–75.Google Scholar
[4] Imkeller, P., Perez-Abreu, V. and Vives, J., Chaos expansion of double intersection local time of Brownian motion in Rd and renormalization, Stoc. Proc. Appl., 56 (1995), no. 1, 1–34.Google Scholar
[5] Nualart, D., Stochastic calculus with respect to fractional brownian motion and applications, Contemporary Mathematics, 336 (2003), 3–39.CrossRefGoogle Scholar
[6] Watanabe, S., Lectures on Stochastic Differential Equations and Malliavin calculus, Springer, 1984.Google Scholar
[7] Xiao, Y. and Zhang, T., Local times of fractional brownian sheets, Prob. Theo. Rela. Fields, 124 (2002), 204–226.Google Scholar