Consider two instances of Brownian motion, B1 and B2. What would the variance of B1 and B2 be? So var(B1+B2)? I know B1 and B2 are not independent but B2-B1 and B1 are.
2026-03-25 09:38:34.1774431514
What is the Variance of Brownian motion
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hint
The variance of $B_1$ and $B_2$ (or more importantly the variance of $B_1$ and $B_2-B_1$) can be read off from the definition of Brownian motion. You are right about which things are independent and which aren't. Observe that $B_1+B_2 = (B_2-B_1) + 2B_1.$