On some results of Cufaro Petroni about Student t-processes

Details On some results of Cufaro Petroni about Student t-processes On some results of Cufaro Petroni about Student t-processes

2008-03-21

arxiv.org/abs/0803.3198v1

Mathematics

Probability

11 pages

Scientific paper

10.1088/1751-8113/41/26/265004

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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