= Gaussian characteristic-function martingale from covariance loss
{c}
{title2=$\exp(iM_t-V_t/2)$}
If a continuous mean <martingale> $M$ and a nonnegative finite-variation process $V$ satisfy $d\langle M\rangle=-dV$, then the <Itô formula> shows $\exp(iM-V/2)$ is a bounded complex <martingale>. Its terminal expectation establishes an entire <Gaussian distribution> with the initial mean and variance. This is stronger than matching only the first two moments in a random-domain field construction.
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