Abstract
In this paper we propose an algorithm to numerically simulate Markov processes of jump type. While these processes can naturally be generated as solutions to jump-SDEs the algorithm we propose is instead based on the interlacing construction of the process. We show that one can construct in the sense of strong convergence a high order numerical scheme based on high order ODE solvers. This result is in sharp contrast to the well known difficulty of constructing high-order numerical schemes for diffusion processes.
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