Regularity of the Local Time for the d-dimensional Fractional Brownian Motion with N-parameters

REFERENCES

• Alòs , E. , O. Mazet , and D. Nualart . 2001 . Stochastic calculus with respect to Gaussian processes . Ann. Prob. 29 ( 2 ): 766 – 801 .
   Web of Science ®Google Scholar
• Ayache , A. , S. Leger , and M. Pontier . 2002 Drap Brownien fractionnaire . Pot. Anal. 17 ( 1 ): 31 – 43 [CROSSREF]
   Web of Science ®Google Scholar
• Bardina , X. , M. Jolis , and C. A. Tudor . 2002 . Weak Convergence to the Fractional Brownian Sheet . Preprint núm. 06/2002 . Universitat Autònoma de Barcelona .
   Google Scholar
• Berman , S. M. 1973 Local nondeterminism and local times of Gaussian processes . Indiana Univ. Math. J. 23 : 69 – 94 . [CROSSREF]
   Web of Science ®Google Scholar
• Coutin , L. , D. Nualart , and C. A. Tudor . 2000 . The Tanaka formula for the fractional Brownian motion . Stoc. Proc. Appl. 94 ( 2 ): 301 – 315 . [CROSSREF]
   Web of Science ®Google Scholar
• Geman , D. and J. Horowitz . 1980 . Occupation densities . Ann. Prob. 8 ( 1 ): 1 – 67
   Web of Science ®Google Scholar
• Hu , Y. , and B. Øksendal . 2002 . Chaos expansion of local time of fractional Brownian motions . Stoc. Anal. Appl. 20 ( 4 ): 815 – 837 . [CROSSREF]
   Web of Science ®Google Scholar
• Hu , Y. , B. Øksendal , and D. M. Salopek . 2001. Weighted Local Time for Fractional Brownian Motion and Applications to Finance . Preprint: http://www.math.uio.no/eprint/pure\_math/2001/13-01.html
   Google Scholar
• Imkeller , P. , and F. Weisz . 1994 . The asymptotic behaviour of local time and occupation integrals of the N-parameter Wiener process in ℝ d . Prob. Theo. Rela. Fields . 98 ( 1 ): 47 – 75 .
   Web of Science ®Google Scholar
• Imkeller , P. , V. Perez–Abreu , and J. Vives . 1995 . Chaos expansion of double intersection local time of Brownian motion in ℝ d and renormalization . Stoc. Proc. Appl. 56 ( 1 ): 1 – 34 . [CROSSREF]
   Web of Science ®Google Scholar
• Lacayo , R. . 2002 . On a Remarkable Integral in the Theory of Fractional Brownian Motion . Preprint núm. 12/2002 . Universitat Autònoma de Barcelona .
   Google Scholar
• Nualart , D. 1995 . The Malliavin calculus and related topics . Prob. and Appl. 21 .
   Google Scholar
• Nualart , D. , and J. Vives . 1992 . Chaos expansions and local times . Pub. Mat. 36 ( 2B ): 827 – 836 .
   Google Scholar
• Nualart , D. , and J. Vives . 1994 . Smoothness of local time and related Wiener functionals . In Chaos Expansions, Multiple Wiener–Itoˆ Integrals and Their Applications , eds. C. Houdré , and V. Pérez–Abreu , 317 – 335 .
   Google Scholar
• Stout , W. 1984 . Almost Sure Convergence . Academic Press .
   Google Scholar
• Watanabe , S. 1984 . Lectures on Stochastic Differential Equations and Malliavin calculus . Springer .
   Google Scholar