Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter Less than 1/2

REFERENCES

• Mandelbrot , B.B. , and Van Ness , J.W. 1968 . Fractional Brownian motions, fractional noises and applications . SIAM Rev. 10 : 422 – 437 . [CSA]
   Web of Science ®Google Scholar
• Young , L.C. 1936 . An inequality of the Hölder type connected with Stieltjes integration . Acta Math. 67 : 251 – 282 . [CSA] [CROSSREF]
   Google Scholar
• Kleptsyna , M.L. , Kloeden , P.E. , and Ahn , V.V. 1998 . Existence and uniqueness theorems for fBm stochastic differential equations . Problems of Inform. Transmission 34 : 332 – 341 . [CSA]
   Google Scholar
• Kubilius , K. 2000 . The existence and uniqueness of the solution of the integral equation driven by fractional Brownian motion . Liet. Mat. Rink. 40 : 104 – 110 . [CSA]
   Google Scholar
• Lin , S.J. 1995 . Stochastic analysis of fractional Brownian motions . Stochastics Stochastics Rep. 55 : 121 – 140 . [CSA]
   Google Scholar
• Ruzmaikina , A.A. 2000 . Stieltjes integrals of Hölder continuous functions with applications to fractional Brownian motion . J. Statist. Phys. 100 : 1049 – 1069 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Zähle , M. 1998 . Integration with respect to fractal functions and stochastic calculus I . Probab. Theory Related Fields 111 : 333 – 374 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Samko , S.G. , Kilbas , A.A. , and Marichev , O.I. 1987. Fractional Integrals and Derivatives: Theory and Applications . Gordon and Breach Science Publishers.
   Google Scholar
• Nualart , D. , and Răşcanu , A. 2002 . Differential equations driven by fractional Brownian motion . Collect. Math. 53 : 55 – 81 . [CSA]
   Google Scholar
• Zähle , M. 2001 . Integration with respect to fractal functions and stochastic calculus II . Math. Nachr. 225 : 145 – 183 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Lyons , T. 1998 . Differential equations driven by rough signals . Rev. Mat. Iberoamericana 14 : 215 – 310 . [CSA]
   Web of Science ®Google Scholar
• Coutin , L. , and Qian , Z. 2000 . Stochastic differential equations for fractional Brownian motions . C.R. Acad. Sci. Paris Sér. I Math. 331 : 75 – 80 . [CSA]
   Google Scholar
• Coutin , L. , and Qian , Z. 2002 . Stochastic analysis, rough paths analysis and fractional Brownian motions . Probab. Theory Related Fields 122 : 108 – 140 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Alòs , E. , León , J.A. , and Nualart , D. 2001 . Stochastic Stratonovich calculus for fractional Brownian motion with Hurst parameter less than 1/2 . Taiwanesse J. Math. 5 : 609 – 632 . [CSA]
   Google Scholar
• León , J.A. , and Tudor , C. 2002 . Semilinear fractional stochastic differential equations . Bol. Soc. Mat. Mexicana 8 : 205 – 226 . [CSA]
   Google Scholar
• Russo , F. , and Vallois , P. 1993 . Forward, backward and symmetric stochastic integration . Probab. Theory Related Fields 97 : 403 – 421 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Shiota , Y. 1986 . A linear stochastic integral equation containing the extended Itô integral . Math. Rep. Toyana Univ. 9 : 43 – 65 . [CSA]
   Google Scholar
• Nualart , D. 2003 . Stochastic integration with respect to fractional Brownian motion and applications . In: Stochastic Models, Proceedings of the Seventh Symposium on Probability and Stochastic Processes . et al. . (eds), Contemporary Mathematics 336 . Amer. Math. Soc. , Providence , RI , 3 – 39 .
   Google Scholar
• Pipiras , V. , and Taqqu , M.S. 2001 . Are classes of deterministic integrands for fractional Brownian motion on an interval complete? Bernoulli 7 : 873 – 897 . [CSA]
   Web of Science ®Google Scholar
• Nualart , D. 1995 . The Malliavin Calculus and Related Topics . Springer-Verlag .
   Google Scholar
• León , J.A. , and Nualart , D. 2005 . An extension of the divergence operator for Gaussian processes . Stochastic Process. Appl. 115 : 481 – 492 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Cheridito , P. , and Nualart , D. 2005 . Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter . Ann. Inst. H. Poincaré Probab. Statist. 41 : 1049 – 1081 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Hu , Y. 2005 . Integral transformations and anticipative calculus for fractional Brownian motions . Mem. Amer. Math. Soc. 175 : 825 . [CSA]
   Web of Science ®Google Scholar
• Decreusefond , L. , and Üstünel , A.S. 1999 . Stochastic analysis of the fractional Brownian motion . Potential Analysis 10 : 177 – 214 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Zähle , M. 1999 . On the link between fractional and stochastic calculus . In: Stochastic Dynamics . Bremen 1997 . Cravel , H. , and Gundlach , M. (eds.), Springer , 305 – 325 .
   Google Scholar