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Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps
Abstract
We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integrability assumptions on the coefficients, we show that the MLP algorithm does not suffer from the curse of dimensionality when approximating the solution of the McKean-Vlasov SDE. The latter means that its computational cost grows at most polynomially in both the state-space dimension of the SDE and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate the practical applicability of the MLP algorithm for two different McKean-Vlasov SDEs in dimensions up to 200.
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BibTeX
@misc{neufeld2026multilevel,
title = {{Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps}},
author = {Ariel Neufeld and Tuan Anh Nguyen and Philipp Schmocker},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10863},
eprint = {2610.10863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10863},
}
RIS
TY - UNPB
TI - Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps
AU - Ariel Neufeld
AU - Tuan Anh Nguyen
AU - Philipp Schmocker
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10863
UR - https://arxiv.org/abs/2610.10863
AB - We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integrability assumptions on the coefficients, we show that the MLP algorithm does not suffer from the curse of dimensionality when approximating the solution of the McKean-Vlasov SDE. The latter means that its computational cost grows at most polynomially in both the state-space dimension of the SDE and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate the practical applicability of the MLP algorithm for two different McKean-Vlasov SDEs in dimensions up to 200.
ER -