I'm familiar with local time $L_t^a$ at level $a$ for a 1-D Brownian motion $B$. I'm reading this paper which talks about a 2D Brownian motion $B$ in a bounded domain $D$ that gets reflected when it hits $\partial D$. They say $$ X_t = X_0 + B_t + \int_0^t n(X_s)dL_s $$
where $n$ is the unit inward normal vector on $\partial D$ and
$L_t$ is the local time process of $X$ on the boundary $\partial D$.
It's intuitively obvious what they are trying to do, but I can't find any reference defining what this local time object is. Can anyone give me a definition and/or a reference which deals with these types of objects?
