Stochastic comparison and preservation of positive correlations for L,vy-type processes

The stochastic comparison and preservation of positive correlations for L,vy-type processes on R (d) are studied under the condition that L,vy measure nu satisfies a <<({0 <|z|a parts per thousand currency sign1})|z||nu(x, dz) - nu(x, d(-z))| < az, x a R (d) , while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary.