On the functional limits for partial sums under stable law

Khurelbaatar Gonchigdanzan , Kamil M. Kosiński

For the partial sums of independent random variables we define a stochastic process and prove that a.s. if and only if , for some sequence and distribution . We also prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables attracted to an -stable law with .

Mots clés: Physical Sciences

Khurelbaatar Gonchigdanzan, Kamil M. Kosiński. On the functional limits for partial sums under stable law. Statistics and Probability Letters, 2009, 79 (17), pp.1818. ⟨10.1016/j.spl.2009.05.004⟩. ⟨hal-00563098⟩