Institut for Matematik

TY - UNPB

T1 - General Υ-transformations

AU - Barndorff-Nielsen, Ole Eiler

AU - Rosinski, Jan

AU - Thorbjørnsen, Steen

N1 - Published in Alea (Rio de Janeiro). 2008;4:131-165.

PY - 2008/2/2

Y1 - 2008/2/2

N2 - In this paper we introduce a general class of transformations of (all or most of) the class ML(Rd), of d-dimensional Lévy measures on Rd, into itself. We refer to transformations of this type as Υ transformations (or Upsilon transformations). Closely associated to these are mappings of the set ID(Rd) of all infinitely divisible laws on Rd into itself. In considerable generality, the mappings are one-to-one, regularising and bi-continuous. Furthermore, in many cases the transformations have a stochastic interpretation in terms of stochastic integrals with respect to Lévy processes.

AB - In this paper we introduce a general class of transformations of (all or most of) the class ML(Rd), of d-dimensional Lévy measures on Rd, into itself. We refer to transformations of this type as Υ transformations (or Upsilon transformations). Closely associated to these are mappings of the set ID(Rd) of all infinitely divisible laws on Rd into itself. In considerable generality, the mappings are one-to-one, regularising and bi-continuous. Furthermore, in many cases the transformations have a stochastic interpretation in terms of stochastic integrals with respect to Lévy processes.

M3 - Working paper

BT - General Υ-transformations

PB - Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet

CY - Århus

ER -