What is the definition of rate of convergence of a sequence of random variables? i.e. what does it mean that the convergence rate of the sequence of random variable $X_1,X_2,\ldots X_n,\ldots$ to $X$ is $g(n)$?
Is the convergence rate unique? Does it depend on the type of convergence?
I thought the definition would be: the convergence rate of $X_1,X_2,\ldots,X_n,\ldots$ to $X$ is $g(n)$ if for large enough $n$, $$ |X_n-X|=O(g(n)) $$