### Abstract

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 α-stable law for α <2. An explicit form is presented in terms of generalized hypergeometric functions when 0 <α <2, α ≠ 1, and that of Fresnel functions S and C for α = 1.

Original language | English |
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Pages (from-to) | 126-135 |

Number of pages | 10 |

Journal | Theory of Probability and its Applications |

Volume | 43 |

Issue number | 1 |

Publication status | Published - Mar 1998 |

### Fingerprint

### Keywords

- Domain of attraction of α-stable law
- Fresnel S and C functions
- Generalized hypergeometric functions
- Limit characteristic function
- Normalized power sums
- Schrödinger equation

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**On the characteristic function of the joint limit distribution of the first- and second-order power sums.** / Michaletzky, Gy; Szeidl, L.; Várlaki, P.

Research output: Contribution to journal › Article

*Theory of Probability and its Applications*, vol. 43, no. 1, pp. 126-135.

}

TY - JOUR

T1 - On the characteristic function of the joint limit distribution of the first- and second-order power sums

AU - Michaletzky, Gy

AU - Szeidl, L.

AU - Várlaki, P.

PY - 1998/3

Y1 - 1998/3

N2 - 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 α-stable law for α <2. An explicit form is presented in terms of generalized hypergeometric functions when 0 <α <2, α ≠ 1, and that of Fresnel functions S and C for α = 1.

AB - 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 α-stable law for α <2. An explicit form is presented in terms of generalized hypergeometric functions when 0 <α <2, α ≠ 1, and that of Fresnel functions S and C for α = 1.

KW - Domain of attraction of α-stable law

KW - Fresnel S and C functions

KW - Generalized hypergeometric functions

KW - Limit characteristic function

KW - Normalized power sums

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=0032235945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032235945&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032235945

VL - 43

SP - 126

EP - 135

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 1

ER -