Date: Feb 12, 2013 11:18 AM
Author: RSimmons
Subject: Random sequence

I'd be grateful if someone can throw light on this: the random sequence X_{2^n + y_n}(omega) -> 0 a.s. for any non-random y_n taking the values on {0,1,...,2^n}. Can be concluded that X_{2^n + Y_n(omega)}(omega) -> 0 a.s. for some random variable Y_n(omega) taking values on{0,1,...,2^n}? Thank you very much.

R. Simmons

Note: X_{2^n + y_n}(omega) means that 2^n + y_n is the index of the sequence.