LIL type behaviour of multivariate Levy processes at zero
Uwe Einmahl
TL;DR
This paper investigates the almost sure behavior of multivariate Levy processes near zero, establishing conditions for their normalized limits and exploring the law of the iterated logarithm and cluster sets.
Contribution
It provides necessary and sufficient conditions for the law of a very slowly varying function and extends the law of the iterated logarithm to multivariate Levy processes at zero.
Findings
Established conditions for the law of a very slowly varying function.
Extended the law of the iterated logarithm to multivariate Levy processes.
Analyzed the cluster set problem for these processes.
Abstract
We study the almost sure behaviour of suitably normalised multivariate Levy processes as t goes to zero. Among other results we find necessary and sufficient conditions for a law of a very slowly varying function which includes a general law of the iterated logarithm in this setting. We also look at the corresponding cluster set problem.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications · Advanced Queuing Theory Analysis