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Perturbation estimates for order-one strong approximations of SDEs without globally monotone coefficients by Dai, Lei; Wang, Xiaojie is a scholarly article available to read on EtoBox.

What is Perturbation estimates for order-one strong approximations of SDEs without globally monotone coefficients about?

To obtain strong convergence rates of numerical schemes, an overwhelming majority of existing works impose a global monotonicity condition on coefficients of SDEs. Nevertheless, there are still many SDEs from applications that do not have globally monotone coefficients. As a recent breakthrough, the authors of [Hutzenthaler, Jentzen, Ann. Probab., 2020] originally presented a perturbation theory for stochastic differential equations (SDEs), which is crucial to recovering strong convergence rates of numerical schemes in a non-globally monotone setting. However, only a convergence rate of order 1/2 was obtained there for time-stepping schemes such as a stopped increment-tamed Euler-Maruyama (SITEM) method. An interesting question arises, also raised by the aforementioned work, as to whether a higher convergence rate than 1/2 can be obtained when higher order schemes are used. The present work attempts to give a positive answer to this question. To this end, we develop some new perturbation estimates that are able to reveal the order-one strong convergence of numerical methods. As the first application of the newly developed estimates, we identify the expected order-one pathwise unifo

Author

Dai, Lei; Wang, Xiaojie

Published

2023

Language

EN