Consider the following one dimensional SDE.
\begin{align*}
dX_t&= \cos( X_t )^\alpha dW(t)\\
X_0&=0
\end{align*}
Consider the equation for \(\alpha >0\). On what interval do you expect to find the solution at all times ? Classify the behavior at the boundaries.
For what values of \(\alpha < 0\) does it seem reasonable to define the process ? any ? justify your answer.
