Abstract
We give a “small time” functional version of Chung’s “other” law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the “other” law of the iterated logarithm at “large times” for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
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This research was partially supported by ARC grants DP0664603 and DP0988483.
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Buchmann, B., Maller, R. The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component. Probab. Theory Relat. Fields 149, 303–330 (2011). https://doi.org/10.1007/s00440-009-0255-1
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DOI: https://doi.org/10.1007/s00440-009-0255-1
Keywords
- Lévy process
- Local behaviour
- Almost sure convergence
- Iterated logarithm laws
- Other law of the iterated logarithm
- Cluster sets
- Functional limit theorem
Mathematics Subject Classification (2000)
- 60G51
- 60F15
- 60F17
- 60F05
- 60J65
- 60J75