Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure

TL;DR

This paper develops an optimal numerical scheme for approximating solutions to infinite-dimensional SDEs with jumps, providing error bounds, complexity analysis, and GPU-based numerical experiments.

Contribution

It introduces a truncated dimension randomized Euler scheme with proven optimality in the IBC framework for SDEs driven by Wiener processes and Poisson jumps.

Findings

The scheme achieves specific error bounds.

The algorithm is proven to be optimal in the IBC sense.

Numerical experiments demonstrate practical efficiency on GPU architecture.

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 $\varepsilon$-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.