Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60E07, 60J45

Retrieve articles in all journals with MSC: 60E07, 60J45


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934885-1
PII: S 0002-9939(1988)0934885-1
Keywords: Stable distributions, stable densities, stable processes
Article copyright: © Copyright 1988 American Mathematical Society