Weak convergence and the Prokhorov radius (Q1191762)

The Prokhorov radius \(D(a,b,t,s)\) is defined as the supremum of the Prokhorov (Ky Fan) distance \[ d(X,a)=\inf\{r>0,\;\text{Pr}(| X- a|>r)<r\} \] over the set \(M(a,b,t,s)\) of real-valued random variables \(X\) with mean \(m\) and variance \(V\) satisfying the inequality constraints \(| m-a|<t\) and \(| V-b|<s\). Using the Kemperman geometric approach to certain moment problems, the author computes the value of \(D(a,b,t,s)\).