ArticleOpen Access

FRACTAL DIMENSION OF FRACTIONAL BROWNIAN MOTION BASED ON RANDOM SETS

RUISHUAI CHAI

Department of Engineering Economics, Henan Institute of Economics and Trade, Zhengzhou, Henan 450018, China

E-mail Address: chairuishuai0206@163.com

https://doi.org/10.1142/S0218348X20400204Cited by:4 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

The fractal dimension of fractional Brownian motion can effectively describe random sets, reflecting the regularity implicit in complex random sets. Data mining algorithms based on fractal theory usually follow the calculation of the fractal dimension of fractional Brownian motion. However, the existing fractal dimension calculation methods of fractal Brownian motion have high time complexity and space complexity, which greatly reduces the efficiency of the algorithm and makes it difficult for the algorithm to adapt to high-speed and massive data flow environments. Therefore, several existing fractal dimension calculation methods of fractional Brownian motion are summarized and analyzed, and a random method is proposed, which uses a fixed memory space to quickly estimate the associated dimension of the data stream. Finally, a comparison experiment with existing algorithms proves the effectiveness of this random algorithm. Second, in the sense of two different measures, based on the principle of stochastic comparison, the stability of the stochastic fuzzy differential equations is derived using the stability of the comparison equations, and the practical stability criterion of two measures according to probability is obtained. Then, the stochastic fuzzy differential equations are discussed. The definition of stochastic exponential stability is given and the stochastic exponential stability criterion is proved.

Keywords:

References

1. L. Song et al., The research of adaptation watershed segmentation based on wavelet transform and fractal dimension, J. Comput. Theor. Nanosci. 13(9) (2016) 6403–6408. Crossref, Google Scholar
2. C. Qingtang, S. Yiran and H. Yijian, Characteristic research of MR damper based on AR model-fractal dimension, Chin. J. Sci. Instrum. 37(12) (2016) 2774–2781. Google Scholar
3. B. Li, Z. Li and P. Li, Spatial and temporal variation characteristics of vegetation cover fractal dimension in Dali River watershed based on GIS and RS, Trans. Chin. Soc. Agricult. Eng. 31(12) (2015) 173–178. Google Scholar
4. Y. Li, L. Yang and Y. Liu, Research on diagnosis algorithm of parkinsons disease based on speech sample multi-edit and random forest, J. Biomed. Eng. 33(2) (2016) 1053–1059. Google Scholar
5. D. I. Gheonea et al., Diagnosis system for hepatocellular carcinoma based on fractal dimension of morphometric elements integrated in an artificial neural network, Biomed. Res. Int. 2014(2) (2015) 239706. Google Scholar
6. W. U. Xiaoxuan, N. I. Zhiwei and N. I. Liping, Research on fractal clustering ensemble algorithm based on cloud computing environment, Comput. Eng. Appl. 30(12) (2015) 69–72. Google Scholar
7. L. Zhang, Z. Qi and L. Guo, Research on online social network information diffusion detection node selection algorithm based on the random walk model, J. Comput. Theor. Nanosci. 13(1) (2016) 971–981. Crossref, Google Scholar
8. Y. Wang, N. Wang and W. Xiao, Research on the evaluation of science and technology award based on random forest and improved ELECTRE-III, Hunan Daxue Xuebao/J. Hunan Univ. Nat. Sci. 42(3) (2015) 140–144. Google Scholar
9. R. Chen and Y. Z. Yang, School of business research on three- dimension promoting model of animation and game industry in China based on the IAP framework, Sci. Technol. Manag. Res. 36(1) (2015) 60–80. Google Scholar
10. Y. Zhu, J. Liu and Y. Xu, Chinese word segmentation research based on conditional random field, Comput. Eng. Appl. 52(15) (2016) 97–100. Google Scholar
11. P. Liu, Research on normal contact stiffness of micro-segments gear based on improved fractal model, J. Mech. Eng. 54(3) (2018) 114. Crossref, Google Scholar
12. N. Wu, W. Gong and S. Han, Experimental research on pseudo-thermal light ghost imaging with random phase plate based on variable motion trail, Acta Opt. Sinica 35(3) (2015) 711005–711024. Google Scholar
13. W. Mo et al., Research on temporal-spatial correlation of power disturbance events based on random matrix theory, High Voltage Eng. 43(3) (2017) 2386–2393. Google Scholar
14. H. Liu, W. Jiang and A. Lam, Research on influence model of fractional calculus derivative Fourier transform on aerobics view image reconstruction, Eur. Phys. J. Plus 134(3) (2019) 234–256. Google Scholar
15. H. Wu and H. Mi, Research on fractal simulation of non-Gaussian fluctuating wind pressure, J. Hunan Univ. 44(3) (2017) 59–68. Google Scholar
16. Y. Jiao, Z. Chen and Y.-N. Liang, Research on QoS quantitative evaluation method of cloud service composition based on Markov process, Comput. Sci. 42(9) (2015) 127–133. Google Scholar
17. T. Wen, M. Song and W. Jiang, Evaluating topological vulnerability based on fuzzy fractal dimension, Int. J. Fuzzy Syst. 20(1) (2018) 31–42. Google Scholar
18. Y. Jin, X. Z. Wu and N. Xie, Real-time filtering research based on on-line modeling random drift of FOG, Guangdian Gongcheng/Opto-Electron. Eng. 42(3) (2015) 13–19. Google Scholar
19. L. Gou, B. Wei and R. Sadiq, Topological vulnerability evaluation model based on fractal dimension of complex networks, PLoS One 11(1) (2016) 146896–146904. Crossref, Web of Science, Google Scholar
20. Z. Zhang, Y. Li and L. Qi, Research on multifractal dimension and improved gray relation theory for intelligent satellite signal recognition, Wireless Netw. (2019) 267–289, https://doi.org/10.1007/s11276-019-02097-1. Google Scholar
21. Z.-Q. Li, J.-J. Zhao and X.-Y. Meng, Research of random laser based on waveguide, Au and ZnO, Chin. J. Luminescence 36(5) (2015) 557–562. Crossref, Google Scholar
22. D.-G. Xu, X.-Y. Xu and X. Chen, Research on improved consensus clustering algorithm based on minkowski distance and its application, J. Hunan Univ. (Nat. Sci.) 43(4) (2016) 133–140. Google Scholar
23. O. V. Chumak and A. S. Rastorguev, Fractal properties of the solar neighborhood based on the geneva-copenhagen survey, Open Astron. 24(1) (2017) 30–42. Crossref, Google Scholar
24. H.-W. Wang, G.-W. Shi and J. Qin, Research on video optical encryption technology in single channel based on chaotic key, J. Optoelectron. Laser 28(9) (2017) 1008–1015. Google Scholar
25. Y. Zhang, X. Wang and Y. Lin, Message forwarding strategy based on markov decision process in opportunistic networks, J. Front. Comput. Sci. Technol. 10(1) (2016) 82–92. Google Scholar
26. R. He, G. Li and Y. Liu, Theoretical analysis and case study on targeted poverty alleviation based on sustainable livelihoods framework: A case study of Liangshan Yi Autonomous Prefecture, Sichuan Province, Progr. Geograp. 36(2) (2017) 613–628. Google Scholar
27. H. Qiu, P. Cui and Y. Wang, Spatial distribution structure of loess landslides and cause analysis based on correlated fractal dimension, Chin. J. Rock Mech. Eng. 34(3) (2015) 546–555. Google Scholar
28. Y. Liu, J. Zhang and F. Bi, Study on fault diagnosis of diesel valve trains based on wigner distribution and fractal dimension, J. Vibrat. Measure. Diagnos. 5 (2016) 523–541. Google Scholar
29. H. Lian, W. Ran and X. Xia, Theoretical research on correlation between microscopic fractal characteristics and macroscopic permeability of sandstone, J. Liaoning Tech. Univ. 36(2) (2017) 624–629. Google Scholar
30. W. Ren, L. Zhao and M. Mu, Study on parameters of random earthquake ground motion model based on current seismic code, World Earthquake Eng. 33(2) (2017) 33–38. Google Scholar

Vol. 28, No. 08

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History

Received 6 January 2020

Accepted 5 March 2020

Published: July 10, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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FRACTAL DIMENSION OF FRACTIONAL BROWNIAN MOTION BASED ON RANDOM SETS

Abstract

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