The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero
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Kamal Hiderah
Abstract
Recently, Mao developed a new explicit method, called the truncated Euler–Maruyama method for nonlinear SDEs, and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The key aim of this paper is to establish the rate of strong convergence of the truncated Euler–Maruyama method for one-dimensional stochastic differential equations involving that the local time at point zero under the drift coefficient satisfies a one-sided Lipschitz condition and plus some additional conditions.
Acknowledgements
We are thankful to the editor and to the anonymous referee for very careful reading and her/his valuable remarks and suggestions which led to the improvement of the article.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Partial information maximum principle for optimal control problem with regime switching in the conditional mean-field model
- 𝕃2-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration
- The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero
- Le Cam–Stratonovich–Boole theory for Itô diffusions
- A chaotic decomposition for the fractional Lebesgue–Pascal noise space
- Lp -solution for BSDEs driven by a Lévy process
- Radonification of a cylindrical Lévy process
Artikel in diesem Heft
- Frontmatter
- Partial information maximum principle for optimal control problem with regime switching in the conditional mean-field model
- 𝕃2-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration
- The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero
- Le Cam–Stratonovich–Boole theory for Itô diffusions
- A chaotic decomposition for the fractional Lebesgue–Pascal noise space
- Lp -solution for BSDEs driven by a Lévy process
- Radonification of a cylindrical Lévy process
