Explicit numerical approximations for McKean-Vlasov neutral stochastic differential delay equations. (English) Zbl 1514.65009
Summary: This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, we obtain that the solution of MV-NSDDE exists and is unique. Then, we use a stochastic particle method, which is on the basis of the results about the propagation of chaos for a stochastic particle system, to deal with the approximation of the law. Furthermore, we construct the tamed Euler-Maruyama numerical scheme with respect to the corresponding particle system and obtain the rate of convergence. Combining propagation of chaos and the convergence rate of the numerical solution to the particle system, we get the convergence error between the numerical solution and exact solution of the original MV-NSDDE in the stepsize and number of particles.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34K40 | Neutral functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
Keywords:
McKean-Vlasov neutral stochastic differential delay equations; super-linear growth; particle system; tamed Euler-Maruyama; strong convergenceReferences:
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