22 citations · 28 across the 4 of their papers we have counts for
4 papers
Structure of shocks in Burgers turbulence with Lévy noise initial data
Joshua Abramson
We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by Lévy noise, or equivalently when the initial potential i…
Lipschitz minorants of Brownian Motion and Levy processes
Joshua Abramson, Steven N. Evans
For , the -Lipschitz minorant of a function is the greatest function such that and $|m(s)-m(t)| \…
Convex minorants of random walks and Lévy processes
Josh Abramson, Jim Pitman, Nathan Ross +1
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and Lévy processes which summarize and extend the literature…
Concave Majorants of Random Walks and Related Poisson Processes
Josh Abramson, Jim Pitman
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchan…