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It's an infinite tape of visualisation of a value $v$, whose increment over time is defined as $$\delta v_t \sim \mathcal{N}(0, t)$$

It's a special case of Martingale's process, for which $$E(X_{n+1} | {\tau}_n) = E(X_n)$$

Or, in other words, no matter at which value $v$ we're right now, the expected value at any future point is equal to $v$.