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

被引：27

作者：

Boufoussi B. ^{[1
]}

Hajji S. ^{[1
]}

Lakhel E.H. ^{[2
]}

机构：

[1] Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University

[2] Department of Mathematics, National School of Applied Sciences Safi, Cadi Ayyad University, Safi

来源：

Afrika Matematika | 2012年 / 23卷 / 2期

关键词：

Fractional Brownian motion; Fractional powers of closed operators; Semigroup of bounded linear operator; Stochastic functional differential equation;

D O I：

10.1007/s13370-011-0028-8

中图分类号：

学科分类号：

摘要：

In this paper, we prove a global existence and uniqueness result of the mild solution for stochastic functional differential equations in Hilbert space driven by a fractional Brownian motion with Hurst parameter H > 1/2. We also study the dependence of the solution on the initial condition. © 2011 African Mathematical Union and Springer-Verlag.

引用

页码：173 / 194

页数：21

共 12 条

[1]

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

[2]

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

[3]

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

[4]

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

[5]

Mandelbrot B.B., van Ness J.W., Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10, 4, pp. 422-437, (1968)

[6]

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

[7]

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

[8]

Nualart D., Rascanu A., Differential equations driven by fractional Brownian motion, Collect. Math., 53, pp. 55-81, (2002)

[9]

Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, Vol. 44, (1983)

[10]

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

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