1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
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| Format: | Preprint |
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2025
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| _version_ | 1866914255842836480 |
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| author | Wang, Shuai Niu, Yuanling Zhang, Ying |
| author_facet | Wang, Shuai Niu, Yuanling Zhang, Ying |
| contents | This paper investigates the strong convergence properties of two Euler-type methods for a class of time-changed stochastic differential equations (TCSDEs) with super-linearly growing drift and diffusion coefficients. Building upon existing research, we propose a backward Euler method (BEM) and introduce its explicit counterpart -- the projected Euler method (PEM). We prove that both methods converge strongly in the $L_2$-sense at the optimal rate of 1/2. This result extends the applicability of both the BEM and the PEM to a broader class of TCSDEs. Moreover, the two methods offer complementary strengths: while BEM possesses wide applicability, PEM is computationally more efficient. Numerical simulations confirm our theoretical findings and illustrate practical performance of both schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients Wang, Shuai Niu, Yuanling Zhang, Ying Numerical Analysis This paper investigates the strong convergence properties of two Euler-type methods for a class of time-changed stochastic differential equations (TCSDEs) with super-linearly growing drift and diffusion coefficients. Building upon existing research, we propose a backward Euler method (BEM) and introduce its explicit counterpart -- the projected Euler method (PEM). We prove that both methods converge strongly in the $L_2$-sense at the optimal rate of 1/2. This result extends the applicability of both the BEM and the PEM to a broader class of TCSDEs. Moreover, the two methods offer complementary strengths: while BEM possesses wide applicability, PEM is computationally more efficient. Numerical simulations confirm our theoretical findings and illustrate practical performance of both schemes. |
| title | 1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.14562 |