Upper and lower limits of doubly perturbed Brownian motion (Q1978134)

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.