Answer by Robert Israel for Examples of stochastic processes that don't exist
A simple attempt to model "white noise" would be a process $W(t)$ on $[0, \infty)$, such that $\int_0^s W(t)\; dt = B(s)$ is a Brownianmotion. But that does not exist because Brownian motion is almost...
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$B_t$ is said to follow a Brownian motion if i) $B_0=0$, ii) $B_t$ is continuous a.s. iii) $B_t$ has independent increments iv) $B_t-B_s\sim N(0,t-s)$. Then Wiener would go on to show that such a...
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