2011/05/06 by Eugen J. Ionaşcu, Eugen J. Ionascu, Richard Stephens +2
Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #26A24 #Aerospace engineering #Classical Analysis and ODEs (math.CA) #Derivative (finance) #Economics #Engineering #FOS: Mathematics #Financial economics #Probabilistic and Robust Engineering Design #Range (aeronautics) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications #math.CA #msc:26A24
paper · pdf · doi:10.48550/arxiv.1105.1373
13 pages, 1 figure
arxiv created 2011/05/06 · openalex publication_date 2011/05/06 · arxiv updated 2011/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we introduce three problems related to the topic of finite Hausdorff moments. Generally speaking, given the first n+1 (n in N or n=0) moments, alpha(0), alpha(1),..., alpha(n), of a real-valued continuously differentiable function f defined on [0,1], what can be said about the size of the image of df/dx? We make the questions more precise and we give answers in the cases of three or fewer moments and in some cases for four moments. In the general situation of n+1 moments, we show that the range of the derivative should contain the convex hull of a set of n numbers calculated in terms of the Bernstein polynomials, xk(1-x)n+1-k, k=1,2,...,n, which turn out to involve expressions just in terms of the given moments alpha(i), i=0,1,2,...n. In the end we make some conjectures about what may be true in terms of the sharpness of the interval range mentioned before.