Operator Semi-Stable Distributions

作者：Cheng Wang; Cheng Wang; Zhihao Ma; Zhihao Ma

来源：STOCHASTIC ANALYSIS AND APPLICATIONS, 2005, 23(4): 659-664.

DOI：10.1081/SAP-200050124

• Lévy measure
• Operator semi-stable

Abstract Jajte introduced the operator semi-stable distributions on R n in [2] and proved an important fact: A full distribution μ is operator semi-stable, if and only if, there exist a number c(0 < c < 1), a vector h ∈ R n , and a nonsingular linear operator B in R n such that the formula μ c  = Bμ*δ(h) holds. In this paper, we make use of the eigenvalue of the matrix B to give a necessary and sufficient condition for ∫|x|≤1|x| r M(dx) < ∞, where M is the Lévy measure of μ. Also, we use the symmetric group of μ to characterize the operators B in (1).

• 单位
  中国计量学院; 浙江大学