Prokhorov Radius of a Neighborhood of Zero Described by Three Moment Constraints
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.
Journal of Global Optimization
Anastassiou, G., & Rychlik, T. (2000). Prokhorov Radius of a Neighborhood of Zero Described by Three Moment Constraints. Journal of Global Optimization, 16 (1), 69-75. https://doi.org/10.1023/a:1008393715273