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Simulation of generalized fractional Brownian motion in C([0,T])

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  • Kozachenko Yuriy

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., 01601Kyiv; and Department of Probability Theory and Mathematical Statistics, Faculty of Mathematics and Information Technology, Vasyl Stus Donetsk National University, 600-Richya Str. 21, 21021 Vinnytsia, Ukraine)

  • Pashko Anatolii

    (Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., 01601Kyiv, Ukraine)

  • Vasylyk Olga

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., 01601Kyiv, Ukraine)

Abstract

In this paper, we construct the model of a generalized fractional Brownian motion with parameter α∈(0,2){\alpha\in(0,2)}, which approximates such a process with given reliability 1-δ{1-\delta}, 0 0{\varepsilon>0} in the space C⁢([0,T]){C([0,T])}. An Example of a simulation in C⁢([0,1]){C([0,1])} is given.

Suggested Citation

  • Kozachenko Yuriy & Pashko Anatolii & Vasylyk Olga, 2018. "Simulation of generalized fractional Brownian motion in C([0,T])," Monte Carlo Methods and Applications, De Gruyter, vol. 24(3), pages 179-192, September.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:3:p:179-192:n:3
    DOI: 10.1515/mcma-2018-0016
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    References listed on IDEAS

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    1. Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
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