Summary
For a bounded linear operator Q, on a Banach space E, and a real number β, there are introduced classes, U β(Q), of some limit distributions such that U O(I coincides with the Lévy class L 0. Elements from U β(Q are characterized in terms of convolution equations and as probability distributions of some random integral functionals. The continuity and fixed points of this random mapping is studied. It is shown that fixed points coincide with the class of Q-stable measures.
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This work partially supported by AFOSR Grant No. F49620 82 C 0009
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Jurek, Z.J. Random integral representations for classes of limit distributions similar to levy class L 0 . Probab. Th. Rel. Fields 78, 473–490 (1988). https://doi.org/10.1007/BF00334208
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DOI: https://doi.org/10.1007/BF00334208