A refined version of the integro-local Stone theorem

Alexander A. Borovkov, Konstantin A. Borovkov

Let $X,X_1,X_2,\dots$ be a sequence of non-lattice i.i.d. random variables with $\mathbf{E}X=0,$ $\mathbf{E}X=1,$ and let $S_n:=X_1+\cdots +X_n$, $n\ge 1.$ We refine Stone's inte…