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A law of iterated logarithm for increasing self-similar Markov processes. (English) Zbl 1053.60027
For an increasing positive self-similar Markov process \(\{X_t, t>0\}\) the functions \(f(\cdot)\) are determined that satisfy relations \(\liminf (X_t/f(t))= c> 0\) a.s. as \(t\to\infty\) or \(t\to 0\), employing the Lamperti bijection between self-similar processes and Lévy processes. Neither stationarity nor independence of increments are required.

MSC:
60F15 Strong limit theorems
60G18 Self-similar stochastic processes
60G17 Sample path properties
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