4 papers
Fokker-Planck Analysis and Invariant Laws for a Continuous-Time Stochastic Model of Adam-Type Dynamics
Kaj Nyström
We develop a continuous-time model for the long-term dynamics of adaptive stochastic optimization, focusing on bias-corrected Adam-type methods. Starting from a finite-sum setting,…
Solvability of the Dirichlet problem for the heat equation implies parabolic uniform rectifiability
Simon Bortz, Steven Hofmann, José MarÃa Martell +1
Let be an open set in space-time with boundary . Under minimal and natural background assumptions - namely, that is time-symmetri…
The Kato square root problem for parabolic operators with an anti-symmetric part in BMO
Alireza Ataei, Kaj Nyström
We solve the Kato square root problem for parabolic operators whose coefficients can be written as the sum of a complex part, which is coercive, and a real anti-symmetric part, whi…
Solvability of the Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph
Simon Bortz, Steven Hofmann, José MarÃa Martell +1
We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic weight with respect to surface measure (w…