A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

Thi-Huong Vu; Hoang-Long Ngo; Duc-Trong Luong; Tran Ngoc Khue

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arXiv · 2411.01849

A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

Thi-Huong Vu·Hoang-Long Ngo·Duc-Trong Luong·Tran Ngoc Khue

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Abstract

We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally H\"older continuous of order $\alpha$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+\alpha)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients.

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Thi-Huong Vu, Hoang-Long Ngo, Duc-Trong Luong, Tran Ngoc Khue. 2024-11-04. A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients. https://arxiv.org/abs/2411.01849

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