Let (B_{t}=left(b_{t}, beta_{t}ight), t geqslant 0) be a (mathrm{BM}^{2}) and (f(x+i y)=u(x, y)+i v(x, y), x, y

Question:

Let $B_{t}=\left(b_{t}, \beta_{t}ight), t \geqslant 0$ be a $\mathrm{BM}^{2}$ and $f(x+i y)=u(x, y)+i v(x, y), x, y \in \mathbb{R}$, an analytic function. If $u_{x}^{2}+u_{y}^{2}=1$, then $\left(u\left(b_{t}, \beta_{t}ight), v\left(b_{t}, \beta_{t}ight)ight), t \geqslant 0$, is a $\mathrm{BM}^{2}$.

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