Approximation of SαS Lévy processes in Lp norm

Abstract

We determine the weak asymptotic behavior of linear and Kolmogorov widths of the S S Lévy process in the Banach spaces L p , p ∈ [1, ∞) for ∈ (0, 2). This complements earlier work by Maiorov and Wasilkowski, who treated the case = 2, i.e., the Wiener process. ResultLet ∈ (0, 2]. Recall that a real-valued random variable is called symmetric -stable (S S) iff for the characteristic function we havê(ii) X 0 = 0 a.s., and X has independent increments. t∈[0,1/c] for any c 1. (iv) X has a.s. cádlàg trajectories, that is, the paths of X are a.s. continuous from the right and convergent from the left in any point.