Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
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Sidorov S. P., Zakharova E. A. On the Error of Approximation by Means of Scenario Trees with Depth 1. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 3, pp. 95-99. DOI: 10.18500/1816-9791-2013-13-3-95-99

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On the Error of Approximation by Means of Scenario Trees with Depth 1

Sidorov Sergei Petrovich, Saratov State University
Zakharova Ekaterina Andreevna, Saratov State University

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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