Abstract
We prove several results on the behavior near t = 0 of Y-t t for certain (0,∞)-valued stochastic processes (Y t)t>0. In particular, we show for Lévy subordinators that the Pareto law on [1,∞) is the only possible weak limit and provide necessary and sufficient conditions for the convergence. More generally, we also consider the weak convergence of tL(Yt) as t →0 for a decreasing function L that is slowly varying at zero. Various examples demonstrating the applicability of the results are presented.
Original language | English |
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Pages (from-to) | 823-835 |
Number of pages | 13 |
Journal | Bernoulli |
Volume | 18 |
Issue number | 3 |
DOIs | |
State | Published - Aug 2012 |
Keywords
- Pareto law
- Regular variation
- Subordinator
- Weak limit theorem
ASJC Scopus subject areas
- Statistics and Probability