Об ошибке приближения деревьями сценариев единичной глубины

Let Λ n denote the set of scenario trees with depth 1 and n scenarios. Let X = (0 ≤ x 1 <... < x n ≤ 1) and let Λ n(X) denote the set of all scenario trees of depth 1 with the scenarios X = (0 ≤ x 1 <... < x n ≤ 1). Let G be a probability distribution defined on [0, 1] and H be a subset of measurable functions defined on [0, 1]. Let d H,X(G) = inf G∈Λ n(X)d H(G,G)and d H(G) = inf G∈Λ nd H(G,G), where d H(G,G) := sup h∈H|∫hdG ∫hdG|. The main goal of the paper is to estimate n d H(G,X) and d H(G) in the case when the set H is a subset of all algebraical polynomials of degree ≤ n. Thus, the paper is examined the error of approximation of a continuous distribution G by means of scenario trees with depth 1 and matching the first n moments.