Let $\emptyset\ne I\subseteq\mathbb R$ be an open interval and $A:C\_0^\infty(I)\to\mathbb R$ be a distribution. Then, $$\langle{\rm D}A,\varphi\rangle:=-\langle A,\varphi'\rangle\;\;\;\text{for }\varphi\in C\_0^\infty(I)$$ is called *distributional derivative* of $A$.

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> Let $B=(B\_t)\_{t\ge 0}$ be a Brownian motion. How is the distributional derivative of $B$ with respect to $t$ defined?
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