Im am looking for literature for the following problem:
Let $X_t$ be an Ito process defined by
$$ dX_t = b(t,X_t)dt+c(t,X_t)dB_t $$
where $b,c:\mathbb{R}_+ \times \mathbb{R} \rightarrow \mathbb{R}$ are Lipschitz-continuous functions in the second variable and $(B_t)$ is the standard Brownian motion. Let $\tau = \inf \left \{ t > 0 \ | \ X_t \in (0,N)^c \right \}$ for some $N > 0$. I want to determine (if possible) $\mathbb{P}(X_{\tau} = N)$.
If you know some usefull literature, or any other tips are really appreciated!
Much thanks in advance