1 problem

Let $L_{t}^{s,x}$ be the local time of $\varphi(s)$ at level $x$. Let $(\mathcal{P}_{y})_{y\geq0}$ be the semigroup and let $\mathcal{P}^{+}_{x}$ and $\mathcal{P}^{-}_{-x}$ be the…