关于Cufaro Petroni关于Student t-过程的一些结果
On some results of Cufaro Petroni about Student t-processes
摘要：
本文讨论Student t过程，如在（Cufaro Petroni N 2007 J. Phys. A，Math. Theor. 40（10），2227-2250）。本文证明和推广了Cufaro Petroni关于Student t-过程的渐近性态及其密度展开式的一些定理。首先，在多元情形下，给出了具有任意实正自由度的Student t-密度的任意实正卷积幂的显式渐近行为;然后，证明了具有奇数自由度的Student t-分布的整数卷积幂是具有奇数自由度的Student t-密度的凸组合.最后，我们证明了这个结果并不推广到非整数卷积幂的情况。
英文摘要：
This paper deals with Student t-processes as studied in (Cufaro Petroni N 2007 J. Phys. A, Math. Theor. 40(10), 2227-2250). We prove and extend some conjectures expressed by Cufaro Petroni about the asymptotical behavior of a Student t-process and the expansion of its density. First, the explicit asymptotic behavior of any real positive convolution power of a Student t-density with any real positive degrees of freedom is given in the multivariate case; then the integer convolution power of a Student t-distribution with odd degrees of freedom is shown to be a convex combination of Student t-densities with odd degrees of freedom. At last, we show that this result does not extend to the case of non-integer convolution powers.
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