Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure

In this paper we deal with pointwise approximation of solutions stochastic differential equations (SDEs) driven by an infinite dimensional Wiener process, additional jumps generated a Poisson random measure. Further investigations contain upper error bounds for the proposed truncated dimension randomized Euler scheme. We also establish matching (up to constants) and lower $\varepsilon$-complexity show that defined algorithm is optimal in information-based complexity (IBC) sense. Finally, results numerical experiments performed via GPU architecture are reported.