On moment sequences and renewal sequences
نویسندگان
چکیده
منابع مشابه
On moment sequences and mixed Poisson distributions
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable X with moment sequence (μs)s∈N we determine a discrete random variable Y , whose moment sequence is given by the Stirling transform of the sequence (μs)s∈N, and identify the distribution as a mixed Poisson distribution. We discuss properti...
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Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1970
ISSN: 0022-247X
DOI: 10.1016/0022-247x(70)90123-x