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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Positivity of stable densities

Authors: S. C. Port and R. A. Vitale
Journal: Proc. Amer. Math. Soc. 102 (1988), 1018-1023
MSC: Primary 60E07; Secondary 60J45
MathSciNet review: 934885
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Abstract: We settle two conjectures of Taylor about the positivity of the densities $ p(t,x)$ of a drift-free, nondegenerate, stable process on $ d$-dimensional Euclidean space $ {R^d}$ starting at the origin. If $ 0 < \alpha < 1$ and $ p(1,0) = 0$, we show that $ x:\;p(t,x) > 0$ for some $ t > 0$ is an open convex cone with vertex 0 and that $ p(t,x) > 0$ for all $ t > 0$ for each $ x$ in this cone. If $ \alpha = 1$ we show that $ p(t,x) > 0$ for all $ t > 0$ and all $ x \in {R^d}$.

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Additional Information

PII: S 0002-9939(1988)0934885-1
Keywords: Stable distributions, stable densities, stable processes
Article copyright: © Copyright 1988 American Mathematical Society

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