Could someone please explain how Brownian motion is predictable? My understanding is that a predictable process is one that depends on information up to time t say but not t itself, therefore W_t has to be observed at time t to determine its value.
2026-04-13 01:37:03.1776044223
How is Brownian motion predictable?
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Brownian motion is continuous in time so you can determine the value of $W_t$ as a limit from the left: $W_t=\lim_{s\rightarrow t^-}W_s$.