678 citations · 994 across the 24 of their papers we have counts for
4 papers · 1 filter
On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients
Prashanta Garain, Kaj Nyström
We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form \begin{equation}\label{abeqn} (\partial_t+X\cdot\nabla_Y)u=\nabla_X\cdot(A(\nabla_X u,X,Y,t)). \end{equati…
Deep learning, stochastic gradient descent and diffusion maps
Carmina Fjellström, Kaj Nyström
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major chal…
Tug-of-war with Kolmogorov
Carmina Fjellström, Kaj Nyström, Matias Vestberg
We introduce a new class of strongly degenerate nonlinear parabolic PDEs $(X,Y,t)\in\mathb…
Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games
Carmina Fjellström, Kaj Nyström, Yuqiong Wang
The fractional heat operator and Continuous Time Random Walks (CTRWs) are interesting and sophisticated mathematical models that can describe complex anomalous…