A Converse to Some Inequalities and Approximations in the Theory of Stieltjes and Stochastic Integrals, and for n-th Derivatives.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The object of this report is to establish by counter-examples the best possible character of theorems recently obtained about stochastic integrals and Stieltjes integrals, and about n-th derivatives and finite differences. The hypotheses involve a pair of estimate functions subject to the convergence of a corresponding integral or Y-series, and it is shown that the divergence of this integral or series render in each case the conclusion false.
- Statistics and Probability