| Abstract: |
| This paper primarily concentrates on Euler schemes for stochastic delay differential equations (SDDEs) with locally Lipschitz coefficients. The convergence in probability and the weak limit process of the normalized error process are derived. Furthermore, this paper consider a specific degenerate stochastic system and obtain the associated weak limit process. In contrast to ``non-degenerate`` systems considered earlier, the normalized error parameter of such degenerate systems is n instead of \sqrt{n}. This caused some challenges, as there are additional terms in the weak limit process. These results are new even for stochastic differential equations without delay. |
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