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Fractional Brownian Motion and Blackbody Radiation
並列摘要
Brownian motion plays a dominant role in the atomic theory of matter and in the atomic theory of electricity. In deriving the law of distribution of energy in the spectrum of blackbody radiation, Planck used a system of cavity oscillators. Hence, it is fitting to investigate if a similar formula can be derived via Brownian motion or a generalization of Brownian motion. In this paper, an alternative radiation formula based on fractional Brownian motion (FBM) is derived. It is comparable to Planck's radiation formula. The only properties that are required in our derivation are the self-similarity and stationary increments of FBM. Consequently, the basic theories of matter, electricity, and radiation are all unified under the same notion of FBM.
並列關鍵字
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延伸閱讀
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- Zhao, S., Liu, Q., Liu, F., & Yin, H. (2013). Sharp Large Deviation for the Energy of α-Brownian Bridge. International Journal of Stochastic Analysis, 2013(), 191-194. https://doi.org/10.1155/2013/952628
- Dai, H., Hu, T. C., & Lee, J. Y. (2014). Operator Fractional Brownian Motion and Martingale Differences. Abstract and Applied Analysis, 2014(), 395-402-1338. https://doi.org/10.1155/2014/791537
- Liu, J. F., Peng, Z. H., Tang, D. L., & Cang, Y. Q. (2012). On the Self-Intersection Local Time of Subfractional Brownian Motion. Abstract and Applied Analysis, 2012(), 1477-1503-296. https://doi.org/10.1155/2012/414195