CHARACTERIZATION OF STRICTLY OPERATOR SEMI-STABLE DISTRIBUTIONS
Gyeong Suk Choi · Journal of the Korean Mathematical Society · 2001
For a linear operator Q from R d into R d and 0 <b< 1, the (Q, b)-semi-stability and the strict (Q, b)-semi-stability of probability measures on R d are defined. The (Q, b)-semi-stability is an extension of operator stability with exponent Q on one hand and of semi-stability with index α and parameter b on the other. Characterization of strictly (Q, b)-semi-stable distributions among (Q, b)-semi-stable distributions is made. Existence of (Q, b)-semi-stable distributions which are not translation of strictly (Q, b)-semi-stable distribution is discussed.