5 citations · 12 across the 12 of their papers we have counts for
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Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps
Ariel Neufeld, Tuan Anh Nguyen, Philipp Schmocker
We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integra…
Neural operators approximate strongly continuous convex monotone semigroups
Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo
We approximate strongly continuous convex monotone semigroups by learning their Chernoff-type one-step operators with neural operators. First, we introduce the general class of so-…
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
Ariel Neufeld, Tuan Anh Nguyen, Philipp Schmocker
We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz ass…
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Ariel Neufeld, Philipp Schmocker, Sizhou Wu
In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks s…