Suppoe that $W(t)$ is a Brownian Motion. I now that if $t \geq s \geq 0$, then $W(t)-W(s)$ is $N(0,t-s)$. Now, suppose that $a \in \mathbb{Z}_+$, then how is distributed $$aW(t)-W(s)?$$ I tried to find in the literature about distributions, but I couldn't find anything.
2026-04-05 23:44:33.1775432673
Question regarding the distribution of $aW(t)-W(s)$
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