I'm wondering if there is a local limit theorem for sums of independent random variables $X_1+X_2+\dots+X_n$ which are independent but not identically distributed? I know some form of CLT holds with the Lyupanov or Lindberg conditions. If $X_1,X_2,\dots$ are integer valued and satisfy Lyupanov or Lindberg conditions (or something similar) do we still get a local limit theorem?
2026-03-28 08:47:08.1774687628
Local limit theorem for not-identically distributed series?
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