# Generalized central limit theorem

I am looking for a generalized central limit theorem for non-square integrable stationary sequences. More precisely I suspect that when $(X_j)_{j\geqslant 1}$ is a stationary sequence such that $X_i$ belongs to the domain of attraction of the $\alpha$-stable law then

$$n^{1/\alpha}\sum_{i=1}^n X_i$$

converges as soon as the dependence of $X_i$ is not too strong (maybe some mixing condition).

Are there results of this sort known? Or maybe I am wrong and my conjecture is false.

• arxiv.org/abs/0906.2717 could interest you. Jun 25 '13 at 21:16
• That's probably what I was looking for. Thx Davide. Jun 26 '13 at 5:53

It gives sufficient conditions on $(X_j)$ in order to ensure the convergence of partial sums divided by $a_n$, where the conditions involve $a_n$. It seems these ones involve $\alpha$-mixing coefficients. Work on $\phi$-mixing coefficient has been performed in