Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients

TL;DR

This paper analyzes the weak convergence of numerical schemes for SDEs with super-linear coefficients, establishing theoretical rates and verifying them through numerical experiments.

Contribution

It provides a general weak error analysis framework for schemes with super-linear growth coefficients, including tamed and balanced schemes.

Findings

Weak convergence rates of half-order for various schemes

Theoretical verification through numerical examples

Extension of Milstein's weak error analysis to super-linear coefficients

Abstract

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of SDEs, we prove a general conclusion on weak convergence of the one-step discretization of the SDEs mentioned above. As applications, we show the weak convergence rates for several numerical schemes of half-order strong convergence, such as tamed and balanced schemes. Numerical examples are presented to verify our theoretical analysis.