ABSTRACT
In this chapter we describe a number of properties of multivariate stable distributions. We start with conditional expectations. Let (X 1, X 2) be symmetric α-stable with 1 < α < 2. We show in Section 4.1 that, as in the Gaussian case, E(X2|X1) is linear in X 1. In fact, E(X2|X1) = cX1 , and the coefficient c equals the normalized covariation of X2 on X1 . (See Chapter 5 for extensions to α ≤ 1 and to the case where (X 1, X 2) is skewed α-stable).
