Unusually large values for spectrally positive stable and related processes. (English) Zbl 0942.60029

Author’s summary: 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.


60G50 Sums of independent random variables; random walks
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