Consider a stochastic process $\mathfrak{ X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{ X}$ at $x$. Suppose furthermore that $\mathfrak{ X}$ can be approximated by discrete time regenerative processes $\mathfrak{ X}^n$ for which $x$ is accesible. We give conditions on $\mathfrak{ X}$ and $\mathfrak{ X}^n$ so that the naturally defined local time of $\mathfrak{ X}^n$ converges weakly to $L$. This limit theorem generalizes previous invariance principles that have appeared in the literature.
Categories: math.PR