3 papers
math.PR2025
Quantitative positivity of transition densities for random perturbations of Hamiltonian systems
Shimaa Elesaely, David P. Herzog, Kyle L. Liss
We study a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assu…
math.PR2025
Phase space contraction of degenerately damped random splittings
David P. Herzog, Jonathan C. Mattingly
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system…
math.PR2024
Small-time asymptotics for hypoelliptic diffusions
Juraj Földes, David P. Herzog
An inductive procedure is developed to calculate the asymptotic behavior at time zero of a diffusion with polynomial drift and degenerate, additive noise. The procedure gives rise…