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In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.
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Differenced Brownian Motion covariance
I am having some difficult showing what the following equals, where $x$ and $y$, $x>y$, distinct times:
$\mathbb{E}[\Delta W_x \Delta W_y]$
where each $\Delta W_t = W_t - W_{t-1}$.
I have decompo …