First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems
2021 ◽
Vol 477
(2245)
◽
pp. 20200258
Keyword(s):
In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.
2018 ◽
Vol 334
◽
pp. 1-17
◽
2009 ◽
Vol 29
(5)
◽
pp. 1113-1127
◽
1998 ◽
Vol 35
(3)
◽
pp. 633-641
◽
Keyword(s):
1999 ◽
Vol 31
(3)
◽
pp. 819-838
◽
2007 ◽
Vol 205
(2)
◽
pp. 949-956
◽
Keyword(s):
1998 ◽
Vol 35
(03)
◽
pp. 633-641
◽
Keyword(s):