Operator-Stable Distribution And Hunt’s Nvpothesis

Operator-stable distributions are the n-dimensional analogues of stable dis-tributions when nousingular matrices are used for scaling. Hunt’s hypothesis mean every semipolar is polar. Every full operator-stable distribution μ has an exponent A such that μt=tAμ*δ(a(t)),where (?)t>0,(?)a:(0,∞)â†'Rn.When the full operator-stable distribution have multiple exponents and its eigenvalues belong to (1/2,1),then operator-stable distributions are satisfied Hunt’s Hypothe-sis.If {Xt} is Levy process and satisfies sector condition.{Zt} be a subordinator with drift β0>0.Then {Yt}={XZt} satisfies sector condition.If {Xt} is Levy process and {Zt} be a subordinator with drift β0>0 satisfying sector condition. Then {Yt}={XZt} satisfies sector condition.