Consider the SDE (stochastic differential equation) as follows:

$$dX_t=X_t\big(b(X_t)dt+a(X_t)dW_t\big)$$

where $b,a:\mathbb R\to\mathbb R$ are Lipschitz and bounded and $W$ is a real-valued Brownian motion. Under which conditions on $r>0, \theta>0$ and $b,a$, one has

$$\mathbb P\big[\exists T>0 \mbox{ such that } |X_t|<r \mbox{ for all } t\in [T,T+\theta]\big]=1?$$