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arXiv · 2303.14748

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

Xiaojie Wang·Yuying Zhao·Zhongqiang Zhang
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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.

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Xiaojie Wang, Yuying Zhao, Zhongqiang Zhang. 2023-03-26. Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients. https://arxiv.org/abs/2303.14748

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