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Convergence of trajectories in fractal interpolation of stochastic processes

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  • Małysz, Robert

Abstract

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, Małysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873–88. [11]], [Małysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415–28. [15]], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171–8. [10]].

Suggested Citation

  • Małysz, Robert, 2006. "Convergence of trajectories in fractal interpolation of stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1328-1338.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1328-1338
    DOI: 10.1016/j.chaos.2005.05.009
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