15. Operator‐Limit Distributions in Probability Theory
The central theme of that monograph are limit distributions in a scheme (1) A n d-valued independent random vectors, A i 's are MATRICES (linear bounded operators) on R d and x i 's are deterministic R d shift vectors. If in (1) one assumes that the triangular array A n X k , 1 ≤ k ≤ n, n ≥ 1, is uniformly infinitesimal then limit distributions are called operator-selfdecomposable. This class includes the classical selfdecomposable measures. For independent and identically distributed X i 's limiting laws are called operator-stable measures. Among them we have the classical and well know stable measures.