Functional differential equations in Hilbert spaces driven by a fractional Brownian motion

Fernique, X.: Regularité des trajectoires des fonctions aléatoires gaussiennes. In: Ecole d’été de Probabilités de Saint-Flour, IV-1974. Lecture Notes in Mathematics, vol. 480, pp. 1–96 (1975)

Ferrante M., Rovira C.: Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H > 1/2. Bernoulli 12(1), 85–100 (2006)

Ferrante, M., Rovira, C.: Convergence of delay differential equations driven by fractional Brownian motion with Hurst parameter H > 1/2. arxiv.org/abs/0903.5498v1

Lyons T.: Differential equations driven by rough signals (I): an extension of an inequality of L. C. Young. Math. Res. Lett. 1, 451–464 (1994)

Mandelbrot B.B., Van Ness J.W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10(4), 422–437 (1968)

Maslowski B., Nualart D.: Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202(1), 277–305 (2003)

Neuenkirch A., Nourdin I., Tindel S.: Delay equations driven by rough paths. Electron. J. Probab. 13, 2031–2068 (2008)

Nualart D., Răşcanu A.: Differential equations driven by fractional Brownian motion. Collect. Math. 53, 55–81 (2002)

Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44. Springer, New York (1983)

Samko S.G., Kilbas A.A., Marichev O.I.: Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, Yvendon (1993)

Young L.C.: An inequality of the Hölder type connected with Stieltjes integration. Acta Math. 67, 251–282 (1936)

Zähle M.: Integration with respect to fractal functions and stochastic calculus. I. Probab. Theory Relat. Fields 111, 333–374 (1998)