Wishart特征函数的改进
Reforming the Wishart characteristic function
摘要：
文献中提出的Wishart分布的特征函数的m次m矩阵作为逆幂的行列式的傅立叶变量，指数是积极的，真正的形状参数。我证明，只有对2 × 2矩阵，这个表达式是明确的-在这种情况下，复杂的范围的行列式排除负实数线。当m大于或等于3时，行列式的值域包含围绕原点的闭合线，因此复对数的单个分支不足以定义行列式的幂。为了解决这个问题，我给出了正确的解析扩展的拉普拉斯变换，通过利用傅里叶-拉普拉斯变换的Wishart过程。
英文摘要：
The literature presents the characteristic function of the Wishart distribution on m times m matrices as an inverse power of the determinant of the Fourier variable, the exponent being the positive, real shape parameter. I demonstrate that only for two times two matrices, this expression is unambiguous -- in this case the complex range of the determinant excludes the negative real line. When m greater or equals 3 the range of the determinant contains closed lines around the origin, hence a single branch of the complex logarithm does not suffice to define the determinant's power. To resolve this issue, I give the correct analytic extension of the Laplace transform, by exploiting the Fourier-Laplace transform of a Wishart process.
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