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Upper and lower limits of doubly perturbed Brownian motion. (English) Zbl 0969.60082
A doubly perturbed Brownian motion behaves as the Brownian motion between its minimum and maximum where it is perturbed. The doubly perturbed Brownian motion arises as a scaling limit of some self-interacting random walks. The authors show how the perturbations affect the asymptotic behaviors of the extrema. Specifically, they prove three theorems which generalize Erdős-Feller-Kolmogorov-Petrowsky, Hirsch, and Chung type integral tests for Brownian motion.

MSC:
60J65 Brownian motion
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