TY - JOUR
T1 - Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations
AU - Aaronson, Jon
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2018.
PY - 2018/5
Y1 - 2018/5
N2 - In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable – and α-rationally ergodic – transformations are presented.
AB - In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable – and α-rationally ergodic – transformations are presented.
KW - Distributional limit
KW - Ergodic stationary process
KW - Infinite ergodic theory
KW - Measure preserving transformation
KW - Normalizing constants
KW - Α-rationally ergodic
UR - http://www.scopus.com/inward/record.url?scp=85046788731&partnerID=8YFLogxK
U2 - 10.1214/17-AIHP825
DO - 10.1214/17-AIHP825
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AN - SCOPUS:85046788731
SN - 0246-0203
VL - 54
SP - 879
EP - 906
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
IS - 2
ER -