Weak convergence analysis of dynamic cutting for Lévy-type processes
DOI:
https://doi.org/10.17721/1812-5409.2026/1.10Keywords:
dynamic cutting, Lévy-driven SDEs, weak convergence, Euler – Maruyama schemeAbstract
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.
Pages of the article in the issue: 78 - 86
Language of the article: English
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