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

  • M. Eddahbi (a1), R. Lacayo (a2), J. L. Solé (a2), J. Vives (a2) and C. A. Tudor (a3)...

Abstract

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.

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References

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[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).
[2] Hu, Y. and Oksendal, B., Chaos expansion of local time of fractional brownian motion, Stochastic Analysis and Applications, 20 (2002), no. 6, 815837.
[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), 4775.
[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, 134.
[5] Nualart, D., Stochastic calculus with respect to fractional brownian motion and applications, Contemporary Mathematics, 336 (2003), 339.
[6] Watanabe, S., Lectures on Stochastic Differential Equations and Malliavin calculus, Springer, 1984.
[7] Xiao, Y. and Zhang, T., Local times of fractional brownian sheets, Prob. Theo. Rela. Fields, 124 (2002), 204226.
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Renormalization Of The Local Time For The d-Dimensional Fractional Brownian Motion With N Parameters

  • M. Eddahbi (a1), R. Lacayo (a2), J. L. Solé (a2), J. Vives (a2) and C. A. Tudor (a3)...

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