On the functional limits for partial sums under stable law

Khurelbaatar Gonchigdanzan, Kamil Marcin Kosiński

For the partial sums $(S_n)$ of independent random variables we define a stochastic process $s_n(t):=(1/d_n){\sum }_{k\le [nt]}(S_k/k-\mu )$ and prove that $$(1/{\log N})\sum_{n\le…