TY - JOUR

T1 - THE INVARIANT AND QUASI-INVARIANT TRANSFORMATIONS OF THE STABLE LÉVY PROCESSES

AU - Smorodina, N.V.

PY - 2007

Y1 - 2007

N2 - Let ξ(t),t [0,1] be a strictly stable Lévy process with the index of stability α (0,2). By Pξ we denote the law of ξ in the Skorokhod space double struck D sign([0,1],ℝd). For arbitrary ξ we construct Pξ -quasi-invariant semigroup of transformations of double struck D sign([0,1],ℝd. Under some nondegeneracy condition on the spectral measure of the stable process we construct Pξ -quasi-invariant group of transformations of double struck D sign([0,1],ℝd). In symmetric case this group is a group of the invariant transformations. © Springer Science + Business Media B.V. 2007.

AB - Let ξ(t),t [0,1] be a strictly stable Lévy process with the index of stability α (0,2). By Pξ we denote the law of ξ in the Skorokhod space double struck D sign([0,1],ℝd). For arbitrary ξ we construct Pξ -quasi-invariant semigroup of transformations of double struck D sign([0,1],ℝd. Under some nondegeneracy condition on the spectral measure of the stable process we construct Pξ -quasi-invariant group of transformations of double struck D sign([0,1],ℝd). In symmetric case this group is a group of the invariant transformations. © Springer Science + Business Media B.V. 2007.

M3 - Article

VL - 97

SP - 239

EP - 250

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

SN - 0167-8019

IS - 1-3

ER -