New York Journal of Mathematics
Volume 7 (2001) 59-69


P. J. Catuogno and S. E. Ferrando

Pointwise Asymptotics for the Jumps of Ergodic Averages

Published: July 1, 2001
Keywords: Cesaro averages. Upcrossing inequalities, Pointwise a.e. convergence, Asymptotics.
Subject: Primary:28D99; secondary:47A35

We study the pointwise asymptotic behaviour for the number of jumps of ergodic averages as the size of the oscillations decreases to zero. The study is carried out in the setting of Chacon-Ornstein averages. We find that under rather general conditions there exists a pointwise almost uniform asymptotics that relates the number and size of the jumps. The proof makes use of Bishop's upcrossing inequalities.


Research partially supported by NSERC

Author information

P. J. Catuogno:
Departamento de Matematicas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, Mar del Plata 7600, Argentina.

S. E. Ferrando:
Department of Mathematics, Physics and Computer Science, Ryerson Polytechnic University, Toronto, Ontario M5B 2K3, Canada.