1959/01/01 by V. P. Leonov, Albert N. Shiryaev, A. N. Shiryaev · 5 citations
Computer Science · Engineering · #Advanced Computational Techniques in Science and Engineering #Advanced Data Processing Techniques #Mathematical Control Systems and Analysis
paper · doi:10.1137/1104031
crossref issued 1959/01/01 · crossref published 1959/01/01 · crossref published-print 1959/01/01 · openalex publication_date 1959/01/01 · crossref created 2005/03/07 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/03
Let η = Q(ξ ) be the polynomial transformation of the random variable ξ . The following rule is introduced in this article in order to calculate the semi-invariants of η from the semi-invariants of ξ . It is necessary 1. to express the moments of η in terms of those of ξ according to (III), 2. to replace in (III) the expression for the moments of ξ with their semi-invariants according to (I.a), 3. to cancel some terms in the expression obtained according to the law formulated in the theorem. By employing this rule in § 4, we have calculated all the semi-invariants of the random function depending quadratically on Laplace’s function.