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Original Articles

A Fractional Donsker Theorem

Pages 328-347 | Received 05 Aug 2013, Accepted 12 Nov 2013, Published online: 28 Feb 2014

References

  • Baudoin , F. , and Nualart , D. 2003 . Equivalence of Volterra processes. Stochastic Process. Appl. 107 ( 2 ): 327 – 350 .
  • Bender , C. , and Parczewski , P. 2010 . Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus. Bernoulli 16 ( 2 ): 389 – 417 .
  • Bender , C. , and Parczewski , P. 2012 . On the Connection between Discrete and Continuous Wick Calculus with an Application to the Fractional Black-Scholes Model . In: Cohen et al. . (Eds.), Stochastic Processes, Filtering, Control and Their Applications , World Scientific .
  • Bender , C. , and Parczewski , P. 2014 . On convergence of S-transforms and a Wiener chaos limit theorem . In preparation .
  • Biagini , F. , Hu , Y. , O ksendal , B. , and Zhang , T. 2008 . Stochastic Calculus for Fractional Brownian Motion and Applications . Probability and its Applications . London : Springer .
  • Billingsley , P. 1968 . Convergence of Probability Measures . New York-London-Sydney-Toronto : John Wiley and Sons, Inc.
  • Bogachev , V.I. 2007 . Measure Theory . Berlin . Springer .
  • Decreusefond , L. , and Üstünel , A.S. 1999 . Stochastic analysis of the fractional Brownian motion . Potential Anal. 10 ( 2 ): 177 – 214 .
  • Decreusefond , L. 2005 . Stochastic integration with respect to Volterra processes . Ann. Inst. H. Poincar Probab. Statist. 41 ( 2 ): 123 – 149 .
  • Gzyl , H. 2006 . An exposé on discrete Wiener chaos expansions . Bol. Asoc. Mat. Venez. 13 ( 1 ): 3 – 27 .
  • Jost , C. 2006 . Transformation formulas for fractional Brownian motion., Stochastic Processes Appl. 116 ( 10 ): 1341 – 1357 .
  • Molchan , G. 1969 . Gaussian processes with spectra which are asy(1986), no.mptotically equivalent to a power of λ. Theory Prob. Appl. 14 : 530 – 532 .
  • Molchan , G. , and Golosov , J. 1969 . Gaussian stationary processes with asymptotic power spectrum. Soviet. Math. Dokl. 10 : 134 – 137 .
  • Mishura , Y. 2008 . Stochastic Calculus for Fractional Brownian Motion and Related Processes . Lecture Notes in Mathematics 1929 . Berlin : Springer .
  • Mishura , Yu.S. , and Rode , S.G. 2007 . Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion. Ukr. Mat. Zh. 59 ( 8 ): 1040 – 1046 . Translation in Ukrainian Math. J. 59 8:1155–1162 (2007) .
  • Nieminen , A. 2004 . Fractional Brownian motion and martingale-differences. Stat. Probab. Lett. 70 ( 1 ): 1 – 10 .
  • Norros , I. , Valkeila , E. , and Virtamo , J. 1999 . An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli 5 ( 4 ): 571 – 587 .
  • Nualart , D. 2006 . The Malliavin Calculus and Related Topics. Edition. , Second Probability and its Applications (New York) . Springer .
  • Privault , N. 2009 . Stochastic Analysis in Discrete and Continuous Settings . Lecture Notes in Mathematics 1982 . Berlin : Springer .
  • Sottinen , T. 2001. Fractional Brownian motion, random walks and binary market models. Finance and Stochastics. 5:343–355.
  • Taqqu , M.S. 1975 . Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheor. Verw. Geb. 31 : 287 – 302 .
  • Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsaa

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