30 citations · 50 across the 4 of their papers we have counts for
5 papers
Weak error analysis for stochastic gradient descent optimization algorithms
Aritz Bercher, Lukas Gonon, Arnulf Jentzen +1
Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization…
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
Christian Beck, Lukas Gonon, Arnulf Jentzen
Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical app…
Risk bounds for reservoir computing
Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error co…
Asset Pricing with General Transaction Costs: Theory and Numerics
Lukas Gonon, Johannes Muhle-Karbe, Xiaofei Shi
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we pro…
Linearized Filtering of Affine Processes Using Stochastic Riccati Equations
Lukas Gonon, Josef Teichmann
We consider an affine process which is only observed up to an additive white noise, and we ask for its law, for some time , conditional on all observations up to this t…