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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A LIL for occupation times of stable processes


Author: Narn-Rueih Shieh
Journal: Proc. Amer. Math. Soc. 100 (1987), 154-158
MSC: Primary 60F17; Secondary 60J30
DOI: https://doi.org/10.1090/S0002-9939-1987-0883420-4
MathSciNet review: 883420
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Abstract: We prove a Strassen-type law of iterated logarithms for the occupation times of an $ {R^d}$-valued $ (d \geq 1)$ stable process with the scaling property and positive density functions. An immediate application of our result is to obtain the asymptotic behavior of the occupation times of a path occupied in large spheres.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0883420-4
Keywords: Stable processes, occupation times, law of iterated logarithms, $ I$-functions
Article copyright: © Copyright 1987 American Mathematical Society