Research Papers

A Practical Approach to Fractional Stochastic Dynamics

[+] Author and Article Information
Tran Hung Thao

Institute of Mathematics,
Vietnam Academy of Science and Technology,
No 18 Hoang Quoc Viet Road,
Nghia Do,
Cau Giay Hanoi 10307, Vietnam
e-mail: thaoth2001@yahoo.com

The generalization of Theorem 1.1 and the Corollary 1.1 are from Dung, N.T., “Class of Fractional Stochastic Differential Equations”, Vietnam J. Math., 36(3), pp. 271–279.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received August 8, 2012; final manuscript received December 16, 2012; published online June 20, 2013. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(3), 031015 (Jul 20, 2013) (6 pages) Paper No: CND-12-1123; doi: 10.1115/1.4023354 History: Received August 08, 2012; Revised December 16, 2012

In this note we present some results on stochastic dynamics with respect to a fractional Brownian motion from a L2-approximation approach. A new and simple definition of fractional stochastic integral is introduced and a theorem of existence and uniqueness for fractional stochastic differential equations is established.

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Kubilius, K., and Melichov, D., 2010, “Quadratic Variations and Estimation of the Hurst Index of the Solution of Stochastic Differential Equations Driven by a Fractional Brownian Motion,” Liathuanian Mathematical Journal, 26(4), pp. 401–417. [CrossRef]
Elliott, R. J., and Van der Hoek, J., 2007, “Ito Formulas for Fractional Brownian Motion,” Advances in Mathematical Finance, XXXVIII, Applied and Numerical Harmonic Analysis, Birkhauser, Boston, Boston MA, pp. 59–81.
Alòs, E., Mazet, O., and NualartD., 2000, “Stochastic Calculus With Respect to Fractional Brownian Motion With Hurst Parameter Less Than 1/2,” Stoch. Process. Appl., 86(1), pp. 121–130. [CrossRef]
Berzino, C., and Léon, J. R., 2008, “Estimation in Models Driven by Fractional Brownian Motion,” Annales de l'Inst. Henri Poincaré de probabilités, Springer-Verlag, Berlin-Heidelberg, 44(2), pp. 191–139. [CrossRef]
Rostek, S., 2009, Option Pricing in Fractional Brownian Motion, Springer.
Marinucci, D., and RobinsonP.M., 1999, “Weak Convergence to Fractional Brownian Motion,” Stoch. Process. Appl., 80, pp. 103–120. [CrossRef]
Dung, N. T., 2011, “Fractional Geometric Mean-Reversion Processes,” J. Math. Anal. Appl., 38(1), pp. 396–402. [CrossRef]
Dung, N. T., 2011, “Semimartingale Approximation of Fractional Brownian Motion and Its Applications,” Comput. Math. Appl., 61(7), pp. 1844–1854. [CrossRef]
Dung, N. T., 2012, “On Delayed Logistic Equation Driven by Fractional Brownian Motions,” ASME J. Comput. Nonlinear Dyn., 7, p. 031005. [CrossRef]
Dung, N. T., 2012, “Mackey-Glass Equation Driven by Fractional Brownian Motion,” Physica A, 391, pp. 5465–5492. [CrossRef]
Dung, N. T., 2013, “Fractional Stochastic Differential Equation With Applications to Finance,” J. Math. Anal. Appl., 397, pp. 334–348. [CrossRef]
Thao, T. H., and ChristineT. A., 2003, “Évolution Des Cours Gouvernée Par un Processus de Type ARIMA Fractionaire,” Studia Babes-Bolyai, Mathematica, 38(2), pp. 107–115.
Thao, T. H., 2006, “An Approximate Approach to Fractional Analysis for Finance,” Nonlinear Anal., 7(1), pp. 124–132. [CrossRef]
Oksendal, B., 2008, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer-Verlag, Berlin-Heidelberg.
Taqqu, M., 2003, “Fractional Brownian Motion and Long-Range Dependence,” Theory and Applications of Long-Range Dependence, Birkhäuser, Boston-Basel-Berlin, pp. 5–38.
Feyel, D., and De la Pradelle, A., 1999, “On Fractional Brownian Motion,” Potential Analysis, 10, pp. 273–288. [CrossRef]






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