Deep neural network approximation for high-dimensional parabolic partial integro-differential equations

Abstract

In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we express the solution in terms of stochastic differential equations (SDEs). Based on several properties of classical estimators, we establish the existence of a DNN that satisfies the necessary assumptions. The results are theoretical and don't have any numerical experiments yet.