$X_n$ is simple random walk
It seems like $E^{F_n}[X_{n+1}^2]=X_n^2+1$
And $E^{F_n}[X_{n+1}^4]=X_n^4+6X_n^2+1$
I think the first expression is due to $X_n^2$ being positve
But how does it reach the second conclusion?
$X_n$ is simple random walk
It seems like $E^{F_n}[X_{n+1}^2]=X_n^2+1$
And $E^{F_n}[X_{n+1}^4]=X_n^4+6X_n^2+1$
I think the first expression is due to $X_n^2$ being positve
But how does it reach the second conclusion?
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