Estimates of stability with respect to the number of summands for distributions of successive sums of independent identically distributed vectors

Andrei Yu. Zaitsev

Let $X_1,\dots ,X_n,\dots$ be i.i.d.\ $d$-dimensional random vectors with common distribution $F$. Then $S_n=X_1+\cdots +X_n$ has distribution $F^n$ (degree is understood in the se…