3. Stochastic arithmetic
From a theoretical point of view, the synchronous implementation of the CESTAC method and the use of random rounding transforms any computer result into a quasi-Gaussian random variable. In this way, we can define a stochastic arithmetic that works on elements that are Gaussian random variables.
3.1 Continuous stochastic arithmetic
This arithmetic works on operands called "stochastic numbers", see
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Definition 1 – stochastic numbers
The set of stochastic numbers is the set of Gaussian random variables. Thus,
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Stochastic arithmetic
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