1
vote
0answers
57 views

Berry-Esseen result for triangular arrays

Let $\{\{X_{n1},\ldots,X_{nn}\},n=1,2,\ldots\}$ be a triangular array of independent random variables where each row contains identically distributed random variables. Let $E[X_{n1}]=\mu_n<\infty$ ...
2
votes
1answer
137 views

Central Limit Theorem for additive function of permutations of sequences

Fix the finite sets $\mathcal{X}$ and $\mathcal{Y}$, and probability mass functions $P_X(x)$ and $P_Y(y)$ on these sets. Assume each value of $P_X(x)$ and $P_Y(y)$ is rational. For each $n$ such ...
4
votes
2answers
364 views

Central Limit Theorem (and Berry-Esseen theorem) for non-independent variables

Consider the triangular array $X_{n,k}$ such that, for each $n>0$, the variables $(X_{n,1},\cdots,X_{n,n})$ have the following properties: For any given $1 \le L \le n$, all subsets of ...
0
votes
0answers
165 views

Convergence of $L^p$ means and/or norms

Dear all, I have a question about convergence of $L^p$-means. It can be shown (Inequalities, Theorem 193, Hardy, Littlewood, Polya) that $\forall f \in L^p(D,\mu)\cap L^\infty(D,\mu), M_p(f) = ...