Consider the equation

\begin{align}

dX_t &= -Y_t dB_t – \frac12 X_t dt\\

dY_t &= X_t dB_t – \frac12 Y_t dt

\end{align}

Let \((X_0,Y_0)=(x,y)\) with \(x^2+y^2=1\). Show that \(X_t^2 + Y_t^2 =1\) for all \(t\) and hence the SDE lives on the unit circle. Does this make intuitive sense ?

# Around the Circle

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