Mixing
Correlation between the first and a random bit of an ergodic binary sequence
$begingroup$
Let $x=(x_1,x_2, ldots) $ be an ergodic random sequence of bits. Let $k $ be a positive integer, and $j $ a random integer uniformly distributed in ${1,ldots, k} $. Is it alway the case that $Cov (x_1,x_i) geq 0$?
Specifically, does the above hold when $x $ is a random rotation of a fixed periodic binary sequence?
probability
asked Jan 25 at 18:23
RonRon
25116
$endgroup$
add a comment |
$begingroup$
Let $x=(x_1,x_2, ldots) $ be an ergodic random sequence of bits. Let $k $ be a positive integer, and $j $ a random integer uniformly distributed in ${1,ldots, k} $. Is it alway the case that $Cov (x_1,x_i) geq 0$?
Specifically, does the above hold when $x $ is a random rotation of a fixed periodic binary sequence?
probability
asked Jan 25 at 18:23
RonRon
25116
$endgroup$
$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13
add a comment |
$begingroup$
Let $x=(x_1,x_2, ldots) $ be an ergodic random sequence of bits. Let $k $ be a positive integer, and $j $ a random integer uniformly distributed in ${1,ldots, k} $. Is it alway the case that $Cov (x_1,x_i) geq 0$?
Specifically, does the above hold when $x $ is a random rotation of a fixed periodic binary sequence?
probability
asked Jan 25 at 18:23
RonRon
25116
$endgroup$
Let $x=(x_1,x_2, ldots) $ be an ergodic random sequence of bits. Let $k $ be a positive integer, and $j $ a random integer uniformly distributed in ${1,ldots, k} $. Is it alway the case that $Cov (x_1,x_i) geq 0$?
Specifically, does the above hold when $x $ is a random rotation of a fixed periodic binary sequence?
probability
probability
asked Jan 25 at 18:23
RonRon
25116
asked Jan 25 at 18:23
RonRon
25116
edited Jan 25 at 18:54
Ron
asked Jan 25 at 18:23
RonRon
25116
asked Jan 25 at 18:23
RonRon
25116
asked Jan 25 at 18:23
RonRon
25116
25116
$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13
add a comment |
$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13
$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13
$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13
add a comment |
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$begingroup$
I've posted the same question on MathOverflow.
$endgroup$
– Ron
Jan 25 at 22:13