Cite this article as:
Sidorov S. P., Zakharova E. A. On the Error of Approximation by Means of Scenario Trees with Depth 1. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 3, pp. 95-99. DOI: https://doi.org/10.18500/1816-9791-2013-13-3-95-99
On the Error of Approximation by Means of Scenario Trees with Depth 1
Let¤n denote the set of scenario trees with depth 1 and n scenarios. LetX = (0 · x1 < . . . < xn · 1) and let¤n(X) denote
the set of all scenario trees of depth 1 with the scenarios X = (0 · x1 < . . . < xn · 1). Let G be a probability distribution
defined on [0, 1] and H be a subset of measurable functions defined on [0, 1]. Let dH,X(G) = inf ˜G∈¤n(X) dH(G, ˜ G) and
dH(G) = inf ˜G∈¤n
dH(G, ˜ G), where dH(G, ˜ G) := suph∈H
¯¯¯
R h dG − R h d˜G
¯¯¯
. The main goal of the paper is to estimate
dH(G,X) and dH(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.
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