Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity

arXiv:2405.05192v1 Announce Type: cross
Abstract: 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 suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) infinite activity. We provide a full error analysis of our so-called random deep splitting method. In particular, we prove that our random deep splitting method converges to the (unique viscosity) solution of the nonlinear …

abstract algorithm analysis arxiv cs.lg cs.na error extension math.na math.pr networks neural networks paper q-fin.mf random solve type