Consider
\begin{align*}
dX_t=& Y_t dB_t + \frac12 X_t dt\\
dY_t=& X_t dB_t + \frac12 Y_t dt
\end{align*}
Show that \(X_t^2-Y_t^2\) is constant for all \(t\).
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Consider
\begin{align*}
dX_t=& Y_t dB_t + \frac12 X_t dt\\
dY_t=& X_t dB_t + \frac12 Y_t dt
\end{align*}
Show that \(X_t^2-Y_t^2\) is constant for all \(t\).
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