In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally astymptotically self-similar, with field or fractional Brownian field with Hurst exposant H. One of the problem, for application of multifractional Brownian motion, is the regularity of the function. In the filtered white noise model the increments are no more homogeneous as in fractional Brownian field case. It is obvious when we consider the tangent field associated with a function. Still the multifractional function in the previous model is constant and it is not convient for many applications. We show the uniform convergence of the series on K. We deduce from the previous questions the almost sure uniform convergence of the series to a mBm.
| Published in | Applied and Computational Mathematics (Volume 9, Issue 6) |
| DOI | 10.11648/j.acm.20200906.14 |
| Page(s) | 195-200 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Multifractional Brownian Motion, Uniform Convergence, Series Expansion
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APA Style
BA Demba Bocar. (2020). Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion. Applied and Computational Mathematics, 9(6), 195-200. https://doi.org/10.11648/j.acm.20200906.14
ACS Style
BA Demba Bocar. Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion. Appl. Comput. Math. 2020, 9(6), 195-200. doi: 10.11648/j.acm.20200906.14
AMA Style
BA Demba Bocar. Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion. Appl Comput Math. 2020;9(6):195-200. doi: 10.11648/j.acm.20200906.14
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Download@article{10.11648/j.acm.20200906.14,
author = {BA Demba Bocar},
title = {Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion},
journal = {Applied and Computational Mathematics},
volume = {9},
number = {6},
pages = {195-200},
doi = {10.11648/j.acm.20200906.14},
url = {https://doi.org/10.11648/j.acm.20200906.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200906.14},
abstract = {In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally astymptotically self-similar, with field or fractional Brownian field with Hurst exposant H. One of the problem, for application of multifractional Brownian motion, is the regularity of the function. In the filtered white noise model the increments are no more homogeneous as in fractional Brownian field case. It is obvious when we consider the tangent field associated with a function. Still the multifractional function in the previous model is constant and it is not convient for many applications. We show the uniform convergence of the series on K. We deduce from the previous questions the almost sure uniform convergence of the series to a mBm.},
year = {2020}
}
TY - JOUR T1 - Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion AU - BA Demba Bocar Y1 - 2020/12/04 PY - 2020 N1 - https://doi.org/10.11648/j.acm.20200906.14 DO - 10.11648/j.acm.20200906.14 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 195 EP - 200 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20200906.14 AB - In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally astymptotically self-similar, with field or fractional Brownian field with Hurst exposant H. One of the problem, for application of multifractional Brownian motion, is the regularity of the function. In the filtered white noise model the increments are no more homogeneous as in fractional Brownian field case. It is obvious when we consider the tangent field associated with a function. Still the multifractional function in the previous model is constant and it is not convient for many applications. We show the uniform convergence of the series on K. We deduce from the previous questions the almost sure uniform convergence of the series to a mBm. VL - 9 IS - 6 ER -
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