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Mackey–Glass equation driven by fractional Brownian motion

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  • Nguyen, Dung Tien

Abstract

In this paper we introduce a fractional stochastic version of the Mackey–Glass model which is a potential candidate to model objects in biology and finance. By a semi-martingale approximate approach we find an semi-analytical expression for the solution.

Suggested Citation

  • Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5465-5472.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5465-5472
    DOI: 10.1016/j.physa.2012.06.013
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    References listed on IDEAS

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    1. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    2. Catherine Kyrtsou & Michel Terraza, 2010. "Seasonal Mackey–Glass–GARCH process and short-term dynamics," Empirical Economics, Springer, vol. 38(2), pages 325-345, April.
    3. Tabak, Benjamin M. & Cajueiro, Daniel O., 2005. "The long-range dependence behavior of the term structure of interest rates in Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 418-426.
    4. Cajueiro, Daniel O. & Tabak, Benjamin M., 2005. "Testing for long range dependence in banking equity indices," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1423-1428.
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    Cited by:

    1. Nguyen Tien, Dung, 2013. "A stochastic Ginzburg–Landau equation with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1962-1971.

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