Consider the radial projection onto the unit sphereof the path a $d$-dimensional Brownian motion $W$,started at the center of the sphere and run for unit time. Given the occupation measure $mu$ of this projectedpath, what can be said about the terminal point $W(1)$, or about therange of the...

The inverse first passage time problem asks whether, for a Brownian motion $B$ and a nonnegative random variable $\zeta$, there exists a time-varying barrier $b$ such that $\mathbb{P}\{B_sb(s),0\leq s\leq t\}=\mathbb{P}\{\zetat\}$. We study a "smoothed" version of this problem and ask whether...

Filiz et al. (2008) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph, where the vertices correspond to the firms and the edges describe the network of interdependencies between the firms, a...