Log-convex and Stieltjes moment sequences
نویسندگان
چکیده
منابع مشابه
Stieltjes Moment Sequences and Positive Definite Matrix Sequences
For a certain constant δ > 0 (a little less than 1/4), every function f : N0 → ]0,∞[ satisfying f(n)2 ≤ δf(n − 1)f(n + 1), n ∈ N, is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence f : N0 → R there is a positive definite matrix sequence (an) which is not of positive type and which satisfies tr(an+2) = f(n), n ∈ N0. For a certain constant ε > 0 (a lit...
متن کاملOn powers of Stieltjes moment sequences, I
For a Bernstein function f the sequence sn = f(1)·. . .·f(n) is a Stieltjes moment sequence with the property that all powers sn, c > 0 are again Stieltjes moment sequences. We prove that sn is Stieltjes determinate for c ≤ 2, but it can be indeterminate for c > 2 as is shown by the moment sequence (n!)c, corresponding to the Bernstein function f(s) = s. Nevertheless there always exists a uniqu...
متن کاملOn powers of Stieltjes moment sequences, II
We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of the moment sequence in analogy to the Lévy-Khintchine representation. We use the result to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. As an applicatio...
متن کاملA transformation from Hausdorff to Stieltjes moment sequences
We introduce a non-linear injective transformation T from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formula T [(an)]n = 1/(a1 · . . . · an). Special cases of this transformation have appeared in various papers on exponential functionals of Lévy processes, partly motivated by mathematical finance. We give several exa...
متن کاملSolution of the Stieltjes Truncated Moment Problem
The conditions of solvability and description of all solutions of the truncated Stieltjes moment problem are obtained using as the starting point earlier results on the Hamburger truncated moment problem. An algebraic algorithm for the explicit solution of both problems is proposed.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2016
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.06.008