Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process

By Sylvain Rubenthaler. 2003

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Jump-adapted discretization schemes for Lévy-driven SDEs (2010, background): “By comparaison, in in the same setting, [21] obtains a convergence rate of only O(λ ( 12− 1 α )∨(−1) ε ).”
A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations (2011, methodology): “The latter process can be efficiently simulated on an arbitrary finite time set and we apply an Euler approximation to get approximative solutions for the stochastic differential equation (see for instance [Rub03] for an analysis of such approximations).”
The approximate Euler method for Lévy driven stochastic differential equations (2005, result): “The results above, starting with (A), are in deep contrast with “pathwise” of convergence obtained for example in [9,5,6], or [14], where one looks for sequences vn increasing to infinity and such that vn(X − X) is tight (as processes, or at some time t) with non-zero limits.”