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

Abstract

In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by an infinite dimensional Wiener process, with additional jumps generated by 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) 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 via GPU architecture are also reported.