Theory of stable stochastic processes and generation of random numbers of stable type

1)Kojo研究了一些二维稳定分布与它们的边缘分布之间的关系。与高斯分布不同的是，他发现存在着与二维分布完全不同的二维稳定分布，但它们在任何方向上共享相同的边缘分布。2）Takenaka提出了一种新的生成稳定随机数的方法。首先，我们必须注意到，通常的计算机程序随机生成方法不能近似稳定分布的重尾。使用“递归调用”技术，我们可以获得比通常方法更好地近似尾部的算法。该算法在2005年3月曼海姆大学2006年3月柏林魏尔斯特拉斯研究所、耶拿大学2006年6月维尔纽斯会议2006年11月东京理和大学Mejo大学2006年3月2006年11月2006年12月200

1) Kojo has investigated the relations between some 2-dimensional stable distributions and their marginal distributions. Different from Gaussian case, he found that there exist 2-dimensional stable distributions which are completely different as 2-dimensional distributions but they share the same marginal distributions in any directions.2) Takenaka proposed a new method of generating stable random numbers. At the first, we have to notice that the usual method of random generation by computer programs can not approximate the heavy tail of the stable distributions. Using the "Recursive Call" technique, we can obtain algorithms which approximate the tail much better than usual methods. More over, the overhead time for the recursive call is only 10%.The results are presented several conferences of colloquims ;2005 March, Manheim University2006 March, Berlin Weierstrass institute, Jena University2006 June Vilnius Conference2006 Nov. Mejo University, Tokyo Rika University