Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure
Probability
2022-05-04 v1 Numerical Analysis
Numerical Analysis
Abstract
In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure. The further investigations contain upper error bounds for the proposed truncated dimension randomized Euler scheme. We also establish matching (up to constants) upper and lower bounds for -complexity and show that the defined algorithm is optimal in the Information-Based Complexity (IBC) sense. Finally, results of numerical experiments performed by using GPU architecture are also reported.
Cite
@article{arxiv.2108.02394,
title = {Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure},
author = {Paweł Przybyłowicz and Michał Sobieraj and Łukasz Stȩpień},
journal= {arXiv preprint arXiv:2108.02394},
year = {2022}
}