On the telegrapher's signals of sticky local times

We consider the boundary trace process of a new class of sticky Brownian motions and study the telegraph signals of the boundary local time. For the fractional telegraph equation \begin{align*} (σ/η) D^α_t v(t,x) + D^{2α}_t v(t,x) = \frac{\partial^2 v}{\partial x^2}(t,x), \quad t>0,\, x \in \mathbb{