UNIVERSITY
OF WROC£AW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 42.1 41.2 41.1 40.2 40.1
39.2 39.1 38.2 38.1 37.2 37.1 36.2
36.1 35.2 35.1 34.2 34.1 33.2 33.1
32.2 32.1 31.2 31.1 30.2 30.1 29.2
29.1 28.2 28.1 27.2 27.1 26.2 26.1
25.2 25.1 24.2 24.1 23.2 23.1 22.2
22.1 21.2 21.1 20.2 20.1 19.2 19.1
18.2 18.1 17.2 17.1 16.2 16.1 15
14.2 14.1 13.2 13.1 12.2 12.1 11.2
11.1 10.2 10.1 9.2 9.1 8 7.2
7.1 6.2 6.1 5.2 5.1 4.2 4.1
3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 33, Fasc. 1,
pages 45 - 63
 

LÉVY MEASURES INVOLVING A GENERALIZED FORM OF FRACTIONAL INTEGRALS

Makoto Maejima
VÍctor Pérez-Abreu
Ken-iti Sato

Abstract: A four-parameter fractional integral transformation Aq,r
  α,p  of measures on ℝd \ (0) is introduced and a systematic study of its properties depending on the values of the parameters is made. Descriptions of its domain, range, and effect on behaviors of measures near or far from the origin are found. A non-commutative relation with a two-parameter Upsilon transformation ϒ
  β,θ  is established in the form ϒ   Aq,r= Aq,rϒ  ′′
  β,θ  α,p    α,p  β,θ for some β′ and θ′ . Then the class of infinitely divisible distributions having Lévy measures of the form Aq,rρ
 α,p is discussed. It is represented as the class of laws of improper stochastic integrals with respect to Lévy processes if - ∞ < α < 1 . For 1 ≤ α < 2 , it is the class of laws of essentially definable improper stochastic integrals.

2000 AMS Mathematics Subject Classification: 60E07, 60H05.

Keywords and phrases: Fractional integral transformation, stochastic integral mapping, Upsilon transformation.

Download:    Abstract    Full text   Abstract + References