Blanchard's bubble process has two regimes, which occur with probability \(\pi\) and \(1-\pi\).
In the first regime, the bubble grows exponentially, whereas in the second regime, the bubble
collapses to a white noise.
With probability \(\pi\):
$$B_{t+1} = \frac{1+r}{\pi}B_t+\epsilon_{t+1}$$
With probability \(1 - \pi\):
$$B_{t+1} = \epsilon_{t+1}$$
where r is a positive constant and \(\epsilon \sim iid(0, \sigma^2)\).