Abstract
We determine the Prokhorov radius of the family of distributions surrounding the Dirac measure at zero whose first, second and fourth moments are bounded by given numbers. This provides the precise relation between the rates of weak convergence to zero and the rate of vanishing of the respective moments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anastassiou, G.A. (1987), The Levy radius of a set of probability measures satisfying basic moment conditions involving {t,t 2}, Constr. Approx. 3, 257–263.
Anastassiou, G.A. (1992), Weak convergence and the Prokhorov radius, J. Math. Anal. Appl. 163, 541–558.
Anastassiou, G.A. and Rachev, S.T. (1992), Moment problems and their applications to characterization of stochastic processes, queuing theory, and rounding problem, in: Approximation Theory, Lecture Notes in Pure and Appl. Math. 138, pp. 1–77. New York: Dekker.
Anastassiou, G.A. and Rychlik, T. (1999), Rates of uniform Prokhorov convergence of probability measures with given three moments to a Dirac one, Comput. Math. Appl., 38, 101–119.
Kemperman, J.H.B. (1968), The general moment problem, a geometric approach, Ann. Math. Statist. 39, 93–122.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anastassiou, G.A., Rychlik, T. Prokhorov Radius of a Neighborhood of Zero Described by Three Moment Constraints. Journal of Global Optimization 16, 33–41 (2000). https://doi.org/10.1023/A:1008381318560
Issue Date:
DOI: https://doi.org/10.1023/A:1008381318560