Thread: sum of dependent random variables

I’m interested in the asymptotic behavior of a sum of dependent random variables. Most of the theorems assume independence between the variables, for example the law of large numbers or Hoeffding’s inequality. One can also assume k-wise independence, which then leads to a k-th power decay in epsilon instead of the quadratic decay given by Hoeffding’s inequality.

I was wondering if there was any more general result that would consider dependent random variables ?

Hey albox.

What kind of attribute are you interested in? I'm not familiar with the epsilon and the context you are using it in.

Are you talking about convergence to distribution? One of the moments? The co-variance terms?