TY - JOUR
T1 - A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
T2 - A flexible split‐step scheme for MV‐SDEs
AU - Chen, Xingyuan
AU - dos Reis, Gonçalo
N1 - Funding Information:
The authors would like to thank the 3 referees for their thorough work and suggestions that led to non trivial improvements.
Publisher Copyright:
© 2022 The Authors
PY - 2022/8/15
Y1 - 2022/8/15
N2 - We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant Lipschitz diffusion coefficient. The scheme is designed to leverage the structure induced by the interacting particle approximation system, including parallel implementation and the solvability of the implicit equation. The scheme attains the classical 1/2 root mean square error (rMSE) convergence rate in stepsize and closes the gap left by [1] regarding efficient implicit methods and their convergence rate for this class of McKean-Vlasov SDEs. A sufficient condition for mean-square contractivity of the scheme is presented. Several numerical examples are presented, including a comparative analysis to other known algorithms for this class (Taming and Adaptive time-stepping) across parallel and non-parallel implementations.
AB - We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant Lipschitz diffusion coefficient. The scheme is designed to leverage the structure induced by the interacting particle approximation system, including parallel implementation and the solvability of the implicit equation. The scheme attains the classical 1/2 root mean square error (rMSE) convergence rate in stepsize and closes the gap left by [1] regarding efficient implicit methods and their convergence rate for this class of McKean-Vlasov SDEs. A sufficient condition for mean-square contractivity of the scheme is presented. Several numerical examples are presented, including a comparative analysis to other known algorithms for this class (Taming and Adaptive time-stepping) across parallel and non-parallel implementations.
KW - Interacting particle systems
KW - McKean-Vlasov equations
KW - Split-step methods
KW - Superlinear growth
UR - http://www.scopus.com/inward/record.url?scp=85129031287&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2022.127180
DO - 10.1016/j.amc.2022.127180
M3 - Article
AN - SCOPUS:85129031287
SN - 0096-3003
VL - 427
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 127180
ER -