Phi-mixing is a strong asymptotic independence condition for a stationary sequence 
. If 
and 
are the sigma-algebras
generated by the past and the future separated by 
steps, define
 |
The sequence is phi-mixing when 
. This controls conditional
probabilities uniformly over past events of arbitrarily small positive probability.
An independent sequence has 
for every 
.
The Ibragimov-Iosifescu conjecture asks whether this mixing condition, finite variance,
and divergence of the variance of partial sums suffice
for a central limit theorem without an additional
rate assumption on 
.
