Abstract:
In this paper, we construct complex-valued random variables that satisfy the usual stability condition, but for a complex stability index α satisfying the conditions |α−1|<1 and |α−12|≠12. A representation of the characteristic functions of the constructed random variables is found, and limit theorems for sums of independent identically distributed random variables are formulated.
Citation:
I. A. Alekseev, “On stable random variables with a complex stability index”, Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021), 5–10; Dokl. Math., 104:3 (2021), 317–321