Multiple sub-fractional integrals and some approximations

References

• Bojdecki , T , Gorostiza , L and Talarczyk , A . 2004 . Sub-fractional Brownian motion and its relation to occupation times . Stat. & Probab. Lett. , 69 : 405 – 419 .
   Web of Science ®Google Scholar
• 2004 . Fractional Brownian density process and its self-intersection local time of order . k, J. Theoret. Probab. , 69 ( 5 ) : 717 – 739 .
   Google Scholar
• 2006 . Limit theorems for occupation time fluctuations of branching systems 1: long-range dependence . Stoch. Proc. Appl. , 116 : 1 – 18 .
   Web of Science ®Google Scholar
• Budhiraja , A . 1997 . “ Multiple stochastic integrals and Hilbert space valued traces with applications to asymptotic statistics and nonlinear filtering ” . In Ph.D. diss. , Chapel Hill : The University of North Carolina .
   Google Scholar
• Budhiraja , A and Kallianpur , G . 1996 . Approximation to the solution of the Zakai equation using multiple Wiener and Stratonovich integral expansions . Stochastics Stochastic Rep. , 56 : 271 – 315 .
   Google Scholar
• 1997 . Two results on multiple Stratonovich integrals . Statistica Sinica , 7 : 907 – 922 .
   Web of Science ®Google Scholar
• Dasgupta , A and Kallianpur , G . 1999 . Chaos decomposition of multiple fractional integrals and applications . Probab. Theory. Relat. Fields , 115 : 505 – 525 .
   Web of Science ®Google Scholar
• 1999 . Multiple fractional integrals . Probab. Theory. Relat. Fields , 115 : 527 – 548 .
   Web of Science ®Google Scholar
• Doukhan , P , Oppenheim , G and Taqqu , M . 2003 . Theory and Applications of Long Range Dependence , Boston : Birkhäuser .
   Google Scholar
• Duncan , T , Hu , Y and Pasik-Dunkan , B . 2000 . Stochastic calculus for fractional Brownian motion I Theory . SIAM J. Control Optim. , 38 ( 2 ) : 582 – 612 .
   Web of Science ®Google Scholar
• Dzhaparide , K and Van Zanten , H . 2004 . A series expansion of fractional Brownian motion . Probab. Theory Relat. Fields , 103 : 39 – 55 .
   Google Scholar
• Hu , Y . 2005 . Integral transformations and anticipative calculus for fractional Brownian motions . Mem. Amer. Math. Soc. , 175 no. 825
   Google Scholar
• Hu , Y and Meyer , PA . 1998 . “ Sur les integrales multiples de Stratonovich ” . In Séminaire de Probabilités XXII, Lecture Notes in Mathematics 1321 , 72 – 81 . Berlin : Springer-Verlag .
   Google Scholar
• Itô , K . 1951 . Multiple Wiener integral . J. Math. Soc. Japan , 3 : 157 – 169 .
   Google Scholar
• Jeon , JW , Lee , KS and Kim , YT . 2004 . A Wong-Zakai type approximation for multiple Wiener-Stratonovich integrals . Stoch. Anal. Appl. , 22 ( 1 ) : 1257 – 1271 .
   Google Scholar
• Johnson , G and Kallianpur , G . 1993 . Homogeneous chaos, p-forms, scaling and the Feynman integral . Trans. Amer. Math. Soc. , 340 : 503 – 548 .
   Web of Science ®Google Scholar
• McKean , HP . 1973 . Wiener's theory of nonlinear noise . In: Stochastic differential equations. Proc. SIAM-AMS , 6 : 191 – 289 .
   Google Scholar
• Mori , T and Oodaira , H . 1986 . The law of the iterated logarithm for self-similar processes represented by multiple Wiener integrals . Probab. Theory Relat. Fields , 71 : 367 – 391 .
   Google Scholar
• Nualart , D . 2006 . The Malliavin Calculus and Related Topics , 2nd , Berlin : Springer-Verlag .
   Google Scholar
• Pérez-Abreu , V and Tudor , C . 2002 . Multiple stochastic fractional integrals: a transfer principle for multiple stochastic fractional integrals. . Bol. Soc. Mat. Mex. , 8 ( 3 ) : 187 – 203 .
   Google Scholar
• Samko , SG , Kilbas , AA and Marichev , OI . 1993 . “ Fractional Integrals and Derivatives ” . In Gordon and Breach Science New York
   Google Scholar
• Solé , JL and Utzet , F . 1990 . Stratonovich integral and trace . Stoch. and Stoch. Reports , 29 : 203 – 220 .
   Google Scholar
• Taqqu , M . 2006 . “ Self-similarity and long-range dependence ” . In 10th Brazilian School of Probability and 2006. Annual Meeting of the Institute of Mathematical Statistics , Rio de Janeiro : IMPA .
   Google Scholar
• Tudor , C and Tudor , M . 2007 . Approximation of multiple Stratonovich fractional integrals . Stoch. Anal. Appl. , 25 : 781 – 799 .
   Web of Science ®Google Scholar
• Tudor , M . 2007 . A strong approximation for double sub-fractional integrals . Appl. Anal. , 86 ( 8 ) : 1037 – 1048 .
   Web of Science ®Google Scholar