ADMISSIBLE PERTURBATIONS OF PROCESSES WITH INDEPENDENTINCREMENTS
Kazuyuki Inoue
Abstract: We investigate conditions on the law equivalence of -valued stochastically
continuous processes with independent increments and with no Gaussian component. This
problem is studied from the standpoint of perturbations. Given two processes
and independent mutually, we put Then
is called an admissible perturbation of if and induce the equivalent
probability measures on the space of sample functions. The class of admissible
perturbations of is described in terms of the time-jump measures and
associated with and respectively. The fine structure of this class is obtained for
processes related to special infinitely divisible distributions such as stable distributions,
distributions of class and their mixtures. A simplified proof is given to the theorem of
Skorokhod on the law equivalence of -valued processes with independent increments.
-valued stochastically
continuous processes with independent increments and with no Gaussian component. This
problem is studied from the standpoint of perturbations. Given two processes 
and 
independent mutually, we put 
Then 
is called an admissible perturbation of 
if 
and 
induce the equivalent
probability measures on the space of sample functions. The class of admissible
perturbations of 
is described in terms of the time-jump measures 
and 
associated with 
and 
respectively. The fine structure of this class is obtained for
processes related to special infinitely divisible distributions such as stable distributions,
distributions of class 
and their mixtures. A simplified proof is given to the theorem of
Skorokhod on the law equivalence of 
-valued processes with independent increments.