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Random integral representations for classes of limit distributions similar to Lévy class L0, II

Published online by Cambridge University Press:  22 January 2016

Zbigniew J. Jurek
Zbigniew J. Jurek*
Affiliation:
Institute of Mathematics, University of Wroclaw, 50384 Wroclaw, Poland
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Let ξ(t) and η(t) be two stochastic processes such that ξ has stationary independent increments and ξ(0) = 0 a.s. Suppose that for each 0 < t ≤ 1, with ξ(tβ) independent of η(t) and a fixed parameter β ∈ (−2, 0). It is shown that ξ(1) satisfies the above equation if and only if ξ(1) is a sum of two independent r.v.’s: strictly stable one with the exponent – β and the one given by a random integral where Y has stationary independent increments and E [|| Y(1)||-β] < ∞.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 114 , June 1989 , pp. 53 - 64
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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