Pointwise Asymptotics for the Jumps of Ergodic Averages

摘要

We study the pointwise asymptoticbehaviour for the number of jumps of ergodic averages as the sizeof the oscillations decreases to zero. The study is carried outin the setting of Chacon-Ornstein averages.We find that under rathergeneral conditions there exists a pointwise almost uniformasymptotics that relates the number and size of the jumps. Theproof makes use of Bishop's upcrossing inequalities.