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概率论与数理统计

2009年

作者：余君武肖艳清

130113

ISBN: (数字)9787564027414

ISBN: (纸本)9787564027414

130113

关键词：数理统计概率论

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Bayes预测问题的统计分析Ⅰ

湘潭师范学院学报（自然科学版） 2009年第2期31卷 17-20页

作者：余君武湖南科技大学数学与计算科学学院湖南湘潭411201

对形状参数β是已知和未知的两种情况,给出了双边截尾AM SAA模型的参数的Bayes点估计和区间估计以及某些统计量的Bayes预测限。

关键词： AM SAA模型 Bayes方法预测限验前分布

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随机波动率下股价服从O-U过程的期权定价

经济数学 2010年第2期27卷 86-89页

作者：朱利芝马鹏余君武湖南科技大学数学与计算科学学院湖南湘潭411201

假设股票价格遵循指数O-U过程,利用随机分析中的鞅方法,得到了具有随机波动率的欧式期权的定价公式,推广了B-S模型.

关键词：期权定价随机波动率 O-U过程

Chaos game representation of functional protein sequences,and simulation and multifractal analysis of induced measures

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Chinese Physics B 2010年第6期19卷 556-568页

作者：喻祖国肖前军石龙余君武 Vo Anh School of Mathematics and Computational Science Xiangtan University School of Mathematical Sciences Queensland University of Technology Department of Mathematics and Computational Science Hunan University of Science and Technology

Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation （CGR） of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems （RIFS） in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq （analogous to specific heat） curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CCRs for different orders to link the functional protein sequences are almost identical if q 〉 0. Finally, the Ca curves of all linked functional proteins resemble a classical phase transition at a critical point.

关键词： chaos game representation recurrent iterated function systems functional proteins multifractal analysis