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Original Articles

Existence and uniqueness for solutions of one dimensional SDE's driven by an additive fractional noise

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Pages 409-427 | Received 04 Sep 2003, Accepted 28 Jul 2004, Published online: 20 Aug 2006

References

References

  • Alòs , E , Mazet , O and Nualart , D . 2001 . Stochastic calculus with respect to Gaussian processes . Ann. Probab. , 29 : 766 – 801 .
  • Arcones , MA . 1995 . On the law of the iterated logarithm for Gaussian processes . J. Theor. Probab. , 8 ( 4 ) : 877 – 904 .
  • Chitashvili , RJ and Toronjadze , TA . 1980/81 . On one-dimensional Stochastic Differential Equations with unit diffusion coefficient, structure of solutions . Stochastics , 4 : 281 – 315 .
  • Coutin , L and Decreusefond , L . 1999 . Abstract nonlinear filtering theory in the presence of fractional Brownian motion . Ann. Appl. Probab. , 9 ( 4 ) : 1058 – 1090 .
  • Decreusefond , L and Üstunel , AS . 1999 . Stochastic analysis of the fractional brownian motion . Potential Anal. , 10 : 177 – 214 .
  • Fernique, X.M. (1974) Regularité des trajectories de fonctions aléatoires gaussiennes. In École d'eté de Saint-Flour IV, Lecture Notes in Mathematics 480, 2–95.
  • Gyöngy , I and Pardoux , E . 1993 . On quasi-linear stochastic partial differential equations . Probab. Theory Rel. Fields , 94 : 413 – 425 .
  • Moret , S and Nualart , D . 2002 . Onsager-Machlup functional for the fractional Brownian motion . Probab. Theory Rel. Fields , 124 : 227 – 260 .
  • Nakao , S . 1972 . On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations . Osaka J. Math. , 9 : 513 – 518 .
  • Norros , I , Valkeila , E and Virtamo , J . 1999 . An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion . Bernoulli , 5 : 571 – 587 .
  • Nualart , D and Ouknine , Y . 2002 . Regularization of Differential equations by fractional noise . Stochast. Proc. Appl. , 102 : 103 – 116 .
  • Ouknine , Y . 1988 . Généralisation d'un Lemme de S. Nakao et Applications . Stochastics , 23 : 149 – 157 .
  • Revuz D Yor M 1999 Continuous Martingale and Brownian Motion, Springer Verlag Berlin–Heidelberg–New York
  • Samko SG Kilbas AA Mariachev OI 1993 Fractional Integrals and Derivatives, Gordon and Breach Science
  • Ju , AVeretennikov . 1981 . On strong solutions and explicit formulas for solutions of stochastic integral equations . Math. USSR Sb. , 39 : 387 – 403 .
  • Zvonkin , AK . 1974 . A transformation of the phase space of a diffusion process that removes the drift . Math. USSR Sb. , 22 : 129 – 149 .

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