{"title":"具有1/ f噪声功率谱的非线性随机微分方程的解","authors":"B. Kaulakys, J. Ruseckas","doi":"10.1109/ICNF.2011.5994297","DOIUrl":null,"url":null,"abstract":"The special nonlinear stochastic differential equations generating power-law distributed signals and 1/ƒ noise are considered. The models involve the generalized Constant Elasticity of Variance (CEV) process, the Bessel process, the Squared Bessel process, and the Cox-Ingersoll-Ross (CIR) process, which are applied for modeling the financial markets, as well. In the paper, 1/ƒβ behavior of the power spectral density is derived directly from the nonlinear stochastic differential equations and the exact solutions for the particular CEV process are presented.","PeriodicalId":137085,"journal":{"name":"2011 21st International Conference on Noise and Fluctuations","volume":"130 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solutions of nonlinear stochastic differential equations with 1/ƒ noise power spectrum\",\"authors\":\"B. Kaulakys, J. Ruseckas\",\"doi\":\"10.1109/ICNF.2011.5994297\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The special nonlinear stochastic differential equations generating power-law distributed signals and 1/ƒ noise are considered. The models involve the generalized Constant Elasticity of Variance (CEV) process, the Bessel process, the Squared Bessel process, and the Cox-Ingersoll-Ross (CIR) process, which are applied for modeling the financial markets, as well. In the paper, 1/ƒβ behavior of the power spectral density is derived directly from the nonlinear stochastic differential equations and the exact solutions for the particular CEV process are presented.\",\"PeriodicalId\":137085,\"journal\":{\"name\":\"2011 21st International Conference on Noise and Fluctuations\",\"volume\":\"130 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 21st International Conference on Noise and Fluctuations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICNF.2011.5994297\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 21st International Conference on Noise and Fluctuations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICNF.2011.5994297","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solutions of nonlinear stochastic differential equations with 1/ƒ noise power spectrum
The special nonlinear stochastic differential equations generating power-law distributed signals and 1/ƒ noise are considered. The models involve the generalized Constant Elasticity of Variance (CEV) process, the Bessel process, the Squared Bessel process, and the Cox-Ingersoll-Ross (CIR) process, which are applied for modeling the financial markets, as well. In the paper, 1/ƒβ behavior of the power spectral density is derived directly from the nonlinear stochastic differential equations and the exact solutions for the particular CEV process are presented.
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