Summary
Let {X t } be aR 1-valued process with stationary independent increments and\(A_t = \mathop {\sup }\limits_{s \leqq t} |X_s |\). In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infA t /h(t)=C a.s. ast→0 andt→∞, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.
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This research is partially supported by Korea Science & Engineering Foundation
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Wee, IS. Lower functions for processes with stationary independent increments. Probab. Th. Rel. Fields 77, 551–566 (1988). https://doi.org/10.1007/BF00959617
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DOI: https://doi.org/10.1007/BF00959617
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Independent Increment
- Lower Function