Singular infinitely divisible distributions whose characteristic functions vanish at infinity

Content Provider	Scilit
Author	Brown, Gavin
Copyright Year	1977
Description	In the course of discussing dynamical systems which enjoy strong mixing but have singular spectrum, E. Hewitt and the author, (2), recently constructed families of symmetric random variables which satisfy inter alia the following properties:(i) $Z_{t}$ is purely singular and has full support,(ii) $χ^{(t)}$(x) → 0 as ± x → ∞, where $χ^{(t)}$ is the characteristic function of $Z_{t}$,(iii)′ $Z_{t+s}$, $Z_{t}$ + $Z_{s}$ have the same null events,(iv) whenever s ≠ t, $Z_{t}$ and $Z_{s}$ + a are mutually singular for every (possibly zero) constant a.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BB611314B65954CAA33C6AC2D06AEC06/S0305004100053913a.pdf/div-class-title-singular-infinitely-divisible-distributions-whose-characteristic-functions-vanish-at-infinity-div.pdf
Ending Page	287
Page Count	11
Starting Page	277
ISSN	03050041
e-ISSN	14698064
DOI	10.1017/s0305004100053913
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Issue Number	2
Volume Number	82
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1977-09-01
Access Restriction	Open
Subject Keyword	Mathematical Proceedings of the Cambridge Philosophical Society Characteristic Functions
Content Type	Text
Resource Type	Article
Subject	Mathematics