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April 1999 Unusually Large Values for Spectrally Positive Stable and Related Processes
George L. O’Brien
Ann. Probab. 27(2): 990-1008 (April 1999). DOI: 10.1214/aop/1022677393


Two classes of processes are considered. One is a class of spectrally positive infinitely divisible processes which includes all such stable processes. The other is a class of processes constructed from the sequence of partial sums of independent identically distributed positive random variables. A condition analogous to regular variation of the tails is imposed. Then a large deviation principle and a Strassen-type law of the iterated logarithm are presented. These theorems focus on unusually large values of the processes. They are expressed in terms of Skorokhod’s $M_1$ topology.


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George L. O’Brien. "Unusually Large Values for Spectrally Positive Stable and Related Processes." Ann. Probab. 27 (2) 990 - 1008, April 1999.


Published: April 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0942.60029
MathSciNet: MR1698995
Digital Object Identifier: 10.1214/aop/1022677393

Primary: 60F10 , 60F20
Secondary: 60G50

Keywords: Infinitely divisible , large deviations , law of the interated logarithm , partial sums , Spectrally positive , Stable processes , the $M_1$ topology

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 2 • April 1999
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