REPRESENTATION OF OPERATOR SEMI-STABLE DISTRIBUTIONS

REPRESENTATION OF OPERATOR SEMI-STABLE DISTRIBUTIONS

For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0<b<1,\; the\; (Q,b,{\alpha})$-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

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