Weak convergence analysis of dynamic cutting for Lévy-type processes
Анотація
We derive weak error bounds for Euler – Maruyama schemes of the one-dimensional Lévy-driven SDE, where small jumps are truncated in a time-dependent way using a dynamic cutting technique. Large jumps are simulated exactly, while small jumps are either (i) omitted or (ii) replaced by a Gaussian term with matching variance. Under standard Lipschitz-growth and smoothness conditions on the coefficients and Lévy measure, we prove that the weak error of both schemes is of order O(n−1). This rate is achieved by choosing the scaling hyperparameter as h = n−α/(ε(2−α)) for (i) and h = n−α/(ε(3−α)) for (ii) respectively.
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