  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.
