Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients

@article{Liu2022ConvergenceAS,
  title={Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients},
  author={Yulong Liu and Yuanling Niu and Xiujun Cheng},
  journal={Appl. Math. Comput.},
  year={2022},
  volume={414},
  pages={126680}
}
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Convergence and stability of the semi-tamed Euler scheme for stochastic differential equations with non-Lipschitz continuous coefficients
The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly…
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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz…
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results…
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TLDR
This paper establishes convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth.
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