Geodesic
On the characteristic function of the joint limit distribution of the first and second order power sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 180-189

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In this paper we investigate the joint limit characteristic function of normalized first and second-order power sums for a sequence of i.i.d. random variables with distributions belonging to the domain of attraction of an $\alpha$-stable law for $\alpha 2$. An explicit form is presented in terms of generalized hypergeometric functions when $0 \alpha 2$, $\alpha\ne 1$, and that of Fresnel functions $S$ and $C$ for $\alpha=1$.
Keywords: normalized power sums, domain of attraction of $\alpha$-stable law, limit characteristic function, generalized hypergeometric functions, Fresnel $S$ and $C$ functions, Schrö, dinger equation. 
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     author = {Gy. Michaletzky and L. Szeidl and P. V\'arlaki},
     title = {On the characteristic function of the joint limit distribution of the first and second order power sums},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {180--189},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a14/}
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Gy. Michaletzky; L. Szeidl; P. Várlaki. On the characteristic function of the joint limit distribution of the first and second order power sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 180-189. http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a14/