Collision local times of two independent fractional Brownian motions

Xiangjun Wang, Jingjun Guo, Guo Jiang

Front. Math. China ›› 2011, Vol. 6 ›› Issue (2) : 325-338.

PDF(198 KB)
PDF(198 KB)
Front. Math. China ›› 2011, Vol. 6 ›› Issue (2) : 325-338. DOI: 10.1007/s11464-011-0095-z
Research Article
RESEARCH ARTICLE

Collision local times of two independent fractional Brownian motions

Author information +
History +

Abstract

In this paper, the collision local times for two independent fractional Brownian motions are considered as generalized white noise functionals. Moreover, the collision local times exist in L 2 under mild conditions and chaos expansions are also given.

Keywords

Fractional Brownian motion / collision local time / white noise functional

Cite this article

Download citation ▾
Xiangjun Wang, Jingjun Guo, Guo Jiang. Collision local times of two independent fractional Brownian motions. Front. Math. China, 2011, 6(2): 325‒338 https://doi.org/10.1007/s11464-011-0095-z

References

[1.]
Albeverio S., Oliveira M., Streit L. Intersection local times of independent Brownian motions as generalized white noise functionals. Acta Appl Math, 2001, 69, 221-241
CrossRef Google scholar
[2.]
Ayache A., Wu D., Xiao Y. Joint continuity of the local times of fractional Brownian sheets. Ann Inst H Poin Prob Stat, 2008, 44, 727-748
CrossRef Google scholar
[3.]
Bender C. An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stoch Processes Appl, 2003, 104, 81-106
CrossRef Google scholar
[4.]
Biagini F., Hu Y., Φksendal B., Zhang T. Stochastic Calculus for Fractional Brownian Motion and Applications, 2008, London: Springer-Verlag
CrossRef Google scholar
[5.]
Drumond C., Oliveira M., Silva J. Bernido C. C., Bernido M. V. Intersection local times of fractional Brownian motions with H ∈ (0, 1) as generalized white noise functionals. 5th Jagna International Workshop Stochastic and Quantum Dynamics of Biomolecular Systems, 2008, Melville: American Institute of Physics 34-45
[6.]
Faria M., Hida T., Streit L., Watanabe H. Intersection local times as generalized white noise functionals. Acta Appl Math, 1997, 46, 351-362
CrossRef Google scholar
[7.]
Guo J, Xiao Y. Multiple intersection local times of fractional Brownian motion. J of Math (to appear)
[8.]
Hu Y. Self-intersection local time of fractional Brownian motions-via chaos expansion. J Math Kyoto Univ, 2001, 41, 233-250
[9.]
Hu Y., Nualart D. Regularity of renormalized self-intersection local time for fractional Brownian motion. Commun Inf Syst, 2007, 7, 21-30
[10.]
Huang Z., Li C. On fractional stable processes and sheets: white noise approach. J Math Anal Appl, 2007, 325, 624-635
CrossRef Google scholar
[11.]
Imkeller P., Yan J. Multiple intersection local time of planar Brownian motion as a particular Hida distribution. J Func Anal, 1996, 140, 256-273
CrossRef Google scholar
[12.]
Jiang Y., Wang Y. On the collision local time of fractional Brownian motions. Chin Ann Math, 2007, 28B, 311-320
[13.]
Marcus M., Rosen J. Additive functionals of several Lévy processes and intersection local times. Ann Prob, 1999, 27, 1643-1678
CrossRef Google scholar
[14.]
Nualart D., Ortiz-Latorre S. Intersection local time for two independent fractional Brownian motions. J Theo Prob, 2007, 20, 759-767
CrossRef Google scholar
[15.]
Obata N. White Noise Calculus and Fock Space, 1994, Berlin: Springer-Verlag.
[16.]
Oliveira M., Silva J., Streit L. Intersection local times of independent fractional Brownian motions as generalized white noise functionals. Acta Appl Math, 2011, 113, 17-39
CrossRef Google scholar
[17.]
Watanabe H. The local time of self-intersections of Brownian motions as generalized Brownian functionals. Lett in Math Phys, 1991, 23, 1-9
CrossRef Google scholar
AI Summary AI Mindmap
PDF(198 KB)

Accesses

Citations

Detail

Sections
Recommended

/