  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.
