depth poset

We know how to compute the density of the bars in the $0$-dimensional persistence diagram for a trajectory of the standard Brownian motion with constant drift $m$, – it is given by\[\frac{4m^2e^{-2m\Delta}(1+e^{-2m\Delta})}{(1-e^{-2m\Delta})^3},\] But what about other drifts? Luckily, we have the theory of scale functions for general Brownian motions (i.e., the processes on the real […]