Convergence rate in \(\mathcal{L}^p\) sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations. (English) Zbl 07797194
Summary: This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in \(\mathcal{L}^p\) sense are revealed, where the convergence rate loses a little due to the proof technique. Then the tamed Euler-Maruyama scheme to the corresponding particle system is established and the convergence rate in \(\mathcal{L}^p\) sense is obtained. Furthermore, combining these two results gives the convergence error in \(\mathcal{L}^p\) sense between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding.
MSC:
| 60Hxx | Stochastic analysis |
| 65Cxx | Probabilistic methods, stochastic differential equations |
| 34Kxx | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
Keywords:
tamed Euler-Maruyama scheme; neutral multiple-delay stochastic McKean-Vlasov equation; strong convergence rate; propagation of chaosReferences:
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