On the algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic

Interval arithmetic and stochastic arithmetic have been both developed for the same purpose, i. e. to control errors coming from floating point arithmetic of computers. Interval arithmetic delivers guaranteed bounds for numerical results whereas stochastic arithmetic provides confidence intervals with known probability. The algebraic properties of stochastic arithmetic are studied with an emphasis on the structure of the set of stochastic numbers. Some new properties of stochastic numbers are obtained based on the comparison with interval arithmetic in midpoint-radius form.

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